[ { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "_private.KomorebiVerification.PacketNaturalityCompletion.0.Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.liftActionHom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.ImageHull.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.seedRank_eq_residue_dimension", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity_le_max", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.activeSources", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.identity_supported_iff_reflexive", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.pure_grouped_fixed_or_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientToNormalForm", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instBEqClaimKind", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom_eq_zero_iff._simp_1_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval_atom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.proj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrowOperator.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.corollaryClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitHull_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization._sizeOf_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorNormedHom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.hasCyclicVector_iff_one_block_per_eigenvalue", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_eq_one_iff_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.proj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.MappedGeneratedHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.restricted_block_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.operatorHull_eq_moduleSpan", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedRank_eq_intrinsicSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm_add_le", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.brecOn.eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.map_operatorHull_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.casesOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.below", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instIsScalarTowerTensorProduct_paperIRelease_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.target_coordinate_active_sum._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM_mkQ", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packet_shortExact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_packet_sum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroRestriction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_restricted_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotient_bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_eq_orbitHull_of_stop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.restrict_diagonal_mul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.recOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.normalFormToQuotient._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.familyGenerates_linearEquiv_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_hasTopologicalSeedRankOne", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.seeds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.ceilDiv_isLeast_generatorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.onePacket._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.norm_coordinateOperator_le", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2082.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.semisimple_seedFinrank_of_decompositions", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictedProjector_bounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues_nonempty", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind._sizeOf_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.queued.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace.ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My_apply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.finiteAlgebra_radicalQuotient_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinate_shortExact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.residueFibre_refinement", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.title", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix_apply_eq_zero_of_lt", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dims", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_map_T", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.merge_fineAddress", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_seedFinrank_eq_maxCeilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPredecessors.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity_le_max", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packetMap_injective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.QuotientModel", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_bound", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorOperator_smul_tmul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.finrank_le_seedRank_of_scalar_quotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FullMatrixCyclicity", "name": "Komorebi.FullMatrixCyclicity.isCyclic_of_ne_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.congr_simp", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.linearMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorOperatorModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedFormalizationStatus.default", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.conjugateEnd", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix_det", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk.inj", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.PacketSpace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorRightTower", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented_quotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.abstractSplitBlockModuleAction", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr.repr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.logPhase_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.rank_le_of_continuous_additive_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.scalar_extension_seedRank_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM_toLinearMap", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum_zero_same", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditioned_coordinate_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedPresentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize_analyze", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.mem_strictSupportIdeal._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_diagonal._proof_1_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.Cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.IdealQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.seed_condition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_not_full_algebra_linear", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_20", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.SCC", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._f", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.idealTop_finite", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_five_copies_rank_three", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.FamilyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.empty_product_rank_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.proj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftTerm._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.parityAddress", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_analysis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraGeneratedHull.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.Foundation.LinearProjectorFamily.mk.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_le_seedFinrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorLeftTowerInstalled", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.weightedDiff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPredecessors", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.complete", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localPureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_ne_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.monic_irreducible_eq_X_sub_C", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_21", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.rightTerm", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.residueAddress", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureChain", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorElim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleExistence", "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_compatible_presentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedRank_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.exists_leftGenerators_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2081.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedNumberLE_iff_operatorAlgebra_family._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_le_norm", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction_action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.imageHull_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.finiteSum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.source_iff_no_incoming_edge", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_diagonal._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_one_seed_insufficient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeDirectSumEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraTransferPattern", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.noConfusion", "runtime_only": false }, { "axioms": [ "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.coordinateProj.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_operator_primary_seed_formula", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.sourceStatus._default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_quotient_projector_norm_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.Satisfied", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.addCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.linearMap", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.exampleClaim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealToPresented_quotient", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.map_eq_top_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.conjectural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.rank_le_of_continuous_semilinear_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.submodule_cyclic_of_hasCyclicVector", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusion_bounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.one_le_conditionNumber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.hasTopologicalSeedRankOne", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.seedRank_eq_radicalTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_span_eq_top", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum._sunfold", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._f", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_direct_sum_rank_two", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.splitProduct_seedFinrank_eq_maxCeilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockAlgEquiv_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_neg", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB_eV\u2083", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_12", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.empty_family_packet_exact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv_symm_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.sourcesFintype._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedFinrank_eq_spectralSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodSndSemilinear._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientLiftCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.mem_graphSpectrum_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.packetProjectors", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeToIdeal_respects", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.range_le_of_surjective_block", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.cyclic_of_minpoly_degree_eq_finrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.proj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.completedRestrictedQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.cyclic_iff_exists_surjective_oneSeedMap._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightTowerInstalled", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.typed_reachability_certificate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraZeroPattern", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concrete", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.space", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv_unique", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm_neg", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetIntersection", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.algebraGeneratedHull_invariant", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "inductive", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.Block", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.exactGraphSeedRank_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_19", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.weightedDiff.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.exists_minimal_fin_family", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.commutes_iff_diagonalProjection", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complexCycleRoot._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.linearMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_scalarImage_membership", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquivRange_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal_underlying", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.injEq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Polyphase.coeffSection", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.actingOperators.congr_simp", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds.eq_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ExactSequences", "name": "Komorebi.PaperIRelease.submodule_quotient_seedRank_bounds", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supported_iff_underlying", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.hasCyclicVector_baseChange_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.annihilate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.splitter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.operatorModule_isTorsion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.module", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.GeneratesWithNSeeds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.finite_packet_equivalent_norm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.generatedAlgebra_preserves_reachable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjector_norm_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "recursor", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localCornerAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.componentProjection", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.leftGenerates_iff_rowsSpan", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotient_bound_operatorNorm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.presentation_action_uniformContinuous", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mixed_natural_is_simple", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.matrixSupported_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_13", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff._sunfold", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.conjecture.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.comp._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_inclusion_ne", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_familyGenerates_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.Generates.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.graph_seedNumber_eq_max_eigenspace_multiplicity", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.equality_pattern_boundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.ImageHull", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqClaimKind._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.exists_pure_generating_set_card_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_nonzero_primary_cyclic._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instSMulCommClassTensorProduct_paperIRelease", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.conjecture", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.infinite_free_quotient_bounds", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.intermediate_same_component", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_minimalCardinality_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceRank", "name": "Komorebi.PaperIRelease.source_component_pureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotient_bounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._aux_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.blockModuleAction", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.coefficient_action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_ker", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureStep", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_7", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.twoCycle_single_component_boundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.partialFormalization.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.restricted_dense", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPackets._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_prod_le_add", "runtime_only": false }, { "axioms": [ "Classical.choice" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.exampleClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.commute", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPackets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketPropagating", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleBlockAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.SixWayCyclicCriterion", "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_iff_invariantFactor_count_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.FamilyGenerates.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.mem_strictSupportIdeal", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.exists_divisionProduct_generators_iff_coordinate_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.familyGenerates_singleton_of_pow_span_eq_top", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr.repr._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.boundedProjector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extension_unique", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.isOpenOrBoundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.eval_intertwining_of_map_T_eq_smul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.target_coordinate_active_sum._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.invariant_of_orbitClosureStep_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.PacketPure", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.exists_full_annihilator_vector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetCompleteSpace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_add", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.actingOperator._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_3", "runtime_only": false }, { "axioms": [ "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_one_seed_insufficient._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_operatorAlgebra_seedRanks", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.maxCount_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorActionsCommuteInstalled", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.lowRankApply_zero_vector", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprClaimRecord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_two_seeds_exist", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrowOperator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_quotient_has_no_nonzero_packets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditionNumber.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.forwardDiff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.mergeAddress", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_tensorProduct_le_mul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.seeded_surjection_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientLiftCLM", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator_inverse", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.splitter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.annihilate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.other_factor_smul_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.cyclic_iff_exists_surjective_oneSeedMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquivRange_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.noConfusionType", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.generates_mono_algebra", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.unique_packet_lift", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqFormalizationStatus", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.map_aggregated_packetRange_eq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.notes", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_of_cyclic._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.classicalInput.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_monotone", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.X", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprClaimKind.repr.match_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complexCycleRoot._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.exponent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.paddedBlockSums_generate", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.StrictPath.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primePower_quotient_subsingleton_of_exponent_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.numericalCertificate", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.operator_preserves_reachable_support", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.toContinuousPacketMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.orbitFamily.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.conjugate_transferBlock", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.IsLowerTriangular", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_nonzero_primary_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq._simp_1_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.declared_relation", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.DH", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.cyclic_iff_seedFinrank_eq_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeToIdeal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.hull_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.ReachableFrom.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_card", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.family_generates_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complex_cycle_seedNumber_isLeast_two._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.singleOperator_operatorAlgebra_seedRanks_eq_of_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.cyclic_four_way_without_polynomial_certificate", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProjectorFamily._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_proj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.IdealTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Foundation.transferBlock_reconstruction_end", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.relationPolynomial.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.idempotentRange_eq_closure_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.generatedAlgebra_le_reachability", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_smul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.exists_source_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.endpoint_isCyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.real_symmetric_matrix_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.BlockMulClosed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.StrictPath", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.operatorAlgebra_seedRank_eq_of_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.componentProjection_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.finrank_le_card_of_generates_of_scalar_factor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.closure_le_ker_of_le_ker", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.familyGenerates_iff_operatorAlgebra_familyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_9", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorElimType", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.target_coordinate_sum", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.RowsSpan.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.assembleIn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.numericalCertificate.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_card_of_component_decomposition._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.adjoint_closed_iff_symmetric", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_lengths_bdd", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Foundation.transferBlock_comp_end", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicityDirectSumEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.actionHom_vertex", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.satisfied_refl._simp_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqFormalizationStatus._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.primary_internal_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.groupedProjection_mem_algebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.star_subalgebra_iff_equivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.NonzeroIndex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.blockApply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.proofTermPresent.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.IdealTop._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.dense_realization", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.blockDiagonalSubalgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.map_algebraOrbitSet", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_components_distinct", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureStep_mono", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedActionEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.PathAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.isBaseChange_endomorphisms", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.seedRank_eq_maxCeilDiv_of_splitProduct_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketDirectSumCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedAction_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_10", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.theoremClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.operator_seedRank_eq_primaryGeneratorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.aeval_map_baseChange", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.intrinsicMultiplicity_le_one_of_primary_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.familyGenerates_iff_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.seedRank_le_of_surjective_intertwining", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.topological_packet_isomorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space.ext", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprClaimKind.repr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.algorithmClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.sourceProjection_comp_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_neg_val", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_apply_coe", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.Source", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.semisimple_seedRank_eq_maxCeilDiv_of_equivalences", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._unsafe_rec", "runtime_only": true }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.exampleClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj_refinement", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.blockModuleAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_My", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_sub_val", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.operatorHull", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_nonzero_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientLiftCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.analyze.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation_eU\u2081", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.sharedSum_familyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mixed_product_not_three", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.operator_continuous", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.sccFintype", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_quotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeeds_generate_of_compression", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.boundaryOnly.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.exists_leftGenerators_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.corner_action_ambient", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate_transport", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.instDecidableEqMonicIrreducibles", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarFactorization", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.seedRank_imageAlgebra_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.singleton_generates_iff_orbitMap_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules_essSurj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_nonneg", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complexCycleRoot.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom_eq_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.generates_univ", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_zero_of_absent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.generatedAlgebra_block_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.natural_seedRank_eq_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mixed_direct_sum_rank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completion_intertwines", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealGrammar", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.actionHom_arrow", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.rhs", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupport_iff_same_class_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.scalarContinuous", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Polyphase.coeffSection.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.H", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.casesOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.contextOnly.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_transferEdge_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.blockModuleAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_add_P1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.transportLimit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.y.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity_le_exactGraphSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.all_preserve_top", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.transferBlock_naturality_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_map_adjacency", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.qj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.map_hull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal_pow_eq_bot", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.maximal_left_ideal_unique", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.casesOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.ctorElim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis_synthesis", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_every_nonzero_is_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_injective", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSum_proj_modK", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.maxCeilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.operator_mem_span_orbit_of_mem", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Polyphase.coeffSection_comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp.injEq", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprClaimRecord.repr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.fullMatrix_module_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.partialFormalization.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.multiplicity_le_of_leftGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.blockApply_zero", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftTerm._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.linearMap_smul_of_intertwining", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range_preimage._abel_1_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.ScalarQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_commutes", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.seeds_subset_orbitClosureIter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strict_mul_power_mem", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetRange_eq_closure_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.IsCyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_7", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.satisfied_trans", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.product_smul_mk", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.operatorWord.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceUpper", "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_sum_local_of_generation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ext_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.U", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.generates_univ", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.SeedNumberLE.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_opNorm_le", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.nonneg_K", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.lifts_generate", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.splitter", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorActionsCommute", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2082", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendedPacketEquivSumQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity_le_of_generates", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.equiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.regular_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictIdeal_power_mem._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.VectorSupported", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "ContinuousLinearMap.codRestrict.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicSpectrumEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.map_mem_span", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component_le_iff._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.corollaryClaim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.queued.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.completedRestrictedQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorOperatorModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM_toLinearMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.encodedDefinition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_def", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.satisfied_postcomp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.maximalStrictSteps_attained", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cyclic_matrix_criterion_of_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.topology", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx_pow_My_pow_unitSeed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.id.elim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedMap_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.activeTargets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.inj", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.quotient_by_whole_is_zero", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.packetPureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetSupport_image_eq_of_single_active", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.source_count_le_packetPureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.merge_is_not_injective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.action_ofAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.one_le_packet_conditionNumber", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.target", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My_eq_multiplication", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.normalFormToQuotient.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.multiplicity_le_of_leftGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.oneBlock_seedRank_eq_ceilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.generatedHull_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.Packet.fibreLinearProjectorFamily.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.classPacketFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_right", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedSpace._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_pos", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.MappedOrbitSet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis_is_eigenbasis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom.noConfusion", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.ctorElim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.closed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_20", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.remarkClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.range_oneSeedMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.transferBlock_pow_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetSupport", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientCompanionBasis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.classicalInput", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.packetPure_discardZeros_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.simple_equiv_natural", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedClaimRecord.default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.comp", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.declared", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.topological_packet_isomorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_11", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_eq_seedFinrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.transferBlock_algorithm_correct", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_21", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModuleInstance", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2081.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMulClosed_of_transitive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.transportColimit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1_not_full_algebra_linear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.transferBlock_comp", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "_private.ReleaseBoundary.0.PaperIBlock08Tests.dims_pos", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packetAnalysis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_operatorAlgebra_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketDirectSumCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.y", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.ctorElim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_8", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.boundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.primary_cyclic_of_hasCyclicVector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicity_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countable_analysis_norm_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionModuleEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.transferBlock_pow_eq_packetPathSum", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.RowsSpan", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_restriction_has_no_nonzero_packets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.class_maximalStrictSteps", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_14", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.unreachable_nonzero_packet_obstruction", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedFinrank.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.leftGenerates_iff_rowsSpan", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.algebraicOrbitHull_le_reachable_support", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.RowsSpan", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.boundary.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.banach_packet_shortExact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion_injective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.radicalTop_seedRank_of_decompositions", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.difficulty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.offdiagonal_zero_of_commutes", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.projectToPacketQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.packetPureSeedRank_discardZeros", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.moduleObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues_bddAbove", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketCoordinates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.elim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.BlockAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.instDecidableEqHeightOneSpectrumPolynomial_paperIRelease", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ExactSequences", "name": "Komorebi.PaperIRelease.shortExact_seedRank_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.directed_two_packet_boundary", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simpleModule", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorLeftTower", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.ordinal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicSeedMaximum_attained", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.below", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_range_preimage", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.norm_le_K_synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infinite_single_packet_rank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.annihilator_two_sided_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.transferGraph_iff_block_ne_zero", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_cauchy", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.packetPureSeedRank_eq_source_count", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Foundation.transferBlock_comp_linearMap", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA_eU\u2081", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorNormedHom._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.companionMatrix", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.proj_eq_self_of_mem_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.directSum_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.fullMatrix_isCyclic_iff_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_unique", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.rightTerm._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules_faithful", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.vectorAnnihilator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.certificateSeeds_generate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.polynomialModule_isTorsion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.groupedProjection_original", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packetMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.PureGenerates._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.FullMatrixCyclicity", "name": "Komorebi.FullMatrixCyclicity.IsCyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_apply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquivRange", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.lhs", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules_full", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_natural_algebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packet_sequence_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.completedFreePresentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.rec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.PreorderClasses", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My_sq_eq_Mx_cube_sub_Mx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supported_rankOne", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.DivisionProductAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency_pow_mulVec_endpoint", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.fullMatrix_every_nonzero_vector_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.cyclic_iff_seedRank_eq_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.operatorAlgebra_seedFinrank_eq_of_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.paddedBlockSum.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedAction.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.diagonalizable_seedNumber_isLeast_of_distinct_eigenvalues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.K", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_analysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.encodedDefinition.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.eq_of_projectors_eq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.remarkClaim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.jacobson_isMaximal", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.mem_vectorAnnihilator._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.quotient", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.topological_reachability_obstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_le_mk_of_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.completedFreePresentation._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.additive_equation_transport", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.presentedToIdeal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.logPhase", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqClaimKind", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.multiplicity_obstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.operator_seedNumber_isLeast_of_polynomialModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.kernelChecked", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_intertwines", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictIdeal_power_mem._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsicSeedMaximum.match_1_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertexWord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec_injective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.PacketSpace.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.algebraicHull.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.prime", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv_apply", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedSpace._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.coordinateOperator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_12", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_arrow", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.encodedDefinition.elim", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.oneBlock_seedFinrank_eq_ceilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.parityAddress._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportPower_eq_bot", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal_ker", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.InvariantFactorCount", "name": "Komorebi.PaperICompletion3.InvariantFactorCount.invariantFactor_operator_seedRanks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.activeSources.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.source", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.discriminant_ne_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpoly_eq_charpoly_of_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ext_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.BlockModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_of_span_eq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.analyze", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_submodule_bounded_equiv_mk", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.IsUpperTriangular", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.image_generates_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.transferBlock_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPackets._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding_dense", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis_rangeAnalysis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedNumber_one_isLeast_of_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.forwardDiff.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_8", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.numericalOnly.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.recOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.multiplicityBlockModuleAction", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.map_closedHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeeds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock_supported", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.restrictScalars_span_operatorAlgebra_eq_span_orbit", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.split_originalRing_top_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.projectToPacketQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.packet_natural_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.curveWeight", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.finiteAmplitude", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.factor_eq_zero_iff_smul", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.local_proj_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom_eq_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.residueProj_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseAmbient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitHull_algorithm_terminates_and_correct", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.transferBlock", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.full_transfer_edge_zero_pattern_correspondence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.spectralSeedMaximum_attained", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorNormedHom._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.seedRank_equiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.mem_vectorAnnihilator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.factor_eq_minpoly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.proj_packet_eq_zero", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.moduleSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_Mx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.coordinate_dist_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlockAlgebra", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues_bddAbove", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOps.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv_isLeast_product_generatorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedFinrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.zero_submodule_packet_exact", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2082", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedRank_eq_geometricSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_eq_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.seedFinrank_eq_idealTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_14", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.regular_columns_literal", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceIsometry", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.numericalOnly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.ofNat_ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.exists_splitProduct_generators_iff_coordinate_bounds", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.PSigma.casesOn._arg_pusher", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.smul_surjective_of_coprime", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.identity_blocks_supported_iff_reflexive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.FamilyGenerates.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_sum_corner", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.block_smul_eq_mul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.source_reachable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.rank_attained", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.mem_graphSpectrum_iff._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.targetNamespace._default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.radicalTop_seedFinrank_of_decompositions", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.id", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.zero_module_rank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedNumber_zero_isLeast_of_subsingleton", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_apply", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1._arg_pusher", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.module", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.PacketBlocks._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.operatorAlgebra_seedRank_eq_one_iff_minpoly_eq_charpoly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeDirectSumEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.ReachableFrom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.annihilate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.Basic", "name": "KomorebiVerification.binomialSquare", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.EigenLabels", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.moduleSeedRank_eq_operatorSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residue_finrank_le_card_of_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraZeroAt", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extended_packet_range", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.image_generates_of_surjective_intertwining", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.finitely_many_monic_primary_components", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix_diagonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_symm_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis_analysis", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.not_seedNumberLE_zero", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.Simple", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_le_of_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.seedFinrank_eq_radicalTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_proj_apply", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_unique", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.rec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.exists_nonzero_packet", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_P1_orthogonal", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.vertex_natural", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn.go", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.maxMultiplicity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.orbit_mem_hull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unary.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_exists_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpoly_degree_eq_finrank_of_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_22", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.AlgebraInvariant", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_diagonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_8", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetInclusion.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mults", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.seedRank_prod_le_left_of_le", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp.noConfusion", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.IsLowerTriangular.add", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infinite_single_source_formula", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.mem_primarySubmodule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.ofNat", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.lemmaClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_synthesizeBlocks", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.rightStep.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorRightModuleInstance", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.seeds_subset_orbitHull", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.MultiplicityModule", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.conjecture.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.MonicIrreducibles", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.StrictPath._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.fintype", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_jacobson_smul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictedProjectorCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signedValues.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx_pow_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.total_liftActionHom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.equivalent_norm_conditioned_coordinates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.numericalCertificate.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_le_norm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_card_of_component_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.transported_isUniformInducing", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenLabelsFintype", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.arrow_corner", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packet_neg_val", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockLinearEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.hull_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_smul_val", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.classPacketFamily.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.splitData", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.finiteAlgebra_radicalQuotient_isSemisimple", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff_two", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_source_boundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_full", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.packetProjection", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.RowsSpan.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.respects", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr.repr._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_iff_minpoly_eq_charpoly", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "_private.PaperIRelease.AlgebraClassGrouping.0.Komorebi.PaperIRelease.strictPath_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.Coefficients", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.NormalForm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.missingSeed.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNorm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.externalInput", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_18", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.Generates.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.propositionClaim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Foundation.end_comp_eq_sum_transferBlock_comps", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My_pow_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.externalInput.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.idempotent_range_fixed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_seedRank_eq_of_bijective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.packet_continuous", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.minpoly_eq_charpoly_iff_all_spectral_multiplicities_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.transferBlock_descends", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.operatorHull", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.diagonalApply.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.parityAddress._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedNumber_isLeast._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrow_corner", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff_three", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.hasCyclicVector_iff_polynomialModule_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryProductQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.dropZeroExponentEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.splitProduct_seedRank_eq_maxCeilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_eq_of_bijective_semilinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeedsEmbedding", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedSpace", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.propositionClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_all_spectral_multiplicities_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.path_endpoint_seedNumber_isLeast_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "inductive", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.submodule_eq_top_of_sources", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates_symm_apply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.multiplicity_seedRank_formula", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packet_norm_eq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.toMatrix_quotientCompanionBasis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.restriction_to_zero_is_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.block_rankOne", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetReachabilityAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.empty_graph_source_boundary", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.comp._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2081", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.classSupport_iff._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.seed_subset_hull._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.multiplicityDirectSumEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB_comp_arrowA", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.transferBlock_preserves_invariant", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.exists_generating_set_card_eq_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_isBounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.seedFinrank_eq_of_exists_fin_family_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.generating_set_meets_source", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_natural_general", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packet_conditioned_coordinate_bounds", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval_id", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.le_orbitClosureStep", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.seedFinrank_eq_residue_finrank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.boundary.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.OperatorWord", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.MatrixSupported.neg", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.hasCyclicVector_iff_oneInvariantFactor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.ctorElimType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.fineAddress", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.hausdorff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.leftGenerates_iff_familyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.generates_univ", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_18", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.projector_mem_generatedAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorActionsCommuteInstalled", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_16", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.MatrixSupported.mul", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.propositionClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.declared", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.generatedAlgebra_hull_le_reachable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.transferBlock_eq_zero_iff_of_bijective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleExistence", "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_finiteAlgebra_seed_formula", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.pathCombinationWord.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraSemiring", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues_nonempty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.generatedAlgebra_unreachable_obstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.relationPolynomial", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.total", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.endpoint", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_minpoly_quotient_presentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.unconditionalNorm_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_of_offdiagonal_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_synthesizeBlocks", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedFormalizationStatus", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.InvariantFactorCount", "name": "Komorebi.PaperICompletion3.InvariantFactorCount.invariantFactorProduct_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.seed_condition", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.total_single", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_vertex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues_nonempty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.indexFintype", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.targetNamespace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.dense_operatorHull_image", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.singleBlock", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.packets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceUpper", "name": "Komorebi.PaperIRelease.localCornerAlgebra.congr_simp", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNormedAddCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_12", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.leftGenerates_iff_familyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.reachable_range_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.MappedGeneratedHull.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.underlying", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.proj_groupedProjection", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.ofSupBound._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.reachable_range_le_in_component", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_freeAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extendPacketFamily._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ext", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.generates_mono", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_end_eq_finrank_blocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_uniform_limit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.reachable_forward", "runtime_only": false }, { "axioms": [ "Classical.choice" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassesFintype._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.lowRankApply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis_bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.support_mul_closed_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.exists_finite_simple_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.projectors._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj_reconstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.coordinates_vertex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.sum_localPureSeedRank_le_of_compression", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.multiplicity_le_of_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.fourCoordinateFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_12", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.finiteSum.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis_norm_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.StrictPath._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.exactGraphSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetSequences._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.partialFormalization", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.exists_multiplicity_presentation", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.proj_mem", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.nil.elim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.horizontal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftStep.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.deleted_zero_rank", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.transferBlockTable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_intertwines", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.banach_packet_shortExact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.PathCombination", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.IsUpperTriangular.add", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_7", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.closedHull._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff._proof_1_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.noConfusion", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.match_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.operator_apply", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_isEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceObstruction", "name": "Komorebi.PaperIRelease.generatedAlgebra_source_obstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.projectorCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryProductQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.componentProjection_mem", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_not_mem_range_arrowA", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.SixWayCyclicCriterion", "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_six_way_algebraicClosure", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.exists_wedderburn_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.freeGrammar", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedClaimKind", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label_injective_of_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.operatorSupported_iff_ambient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.all_pure_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_eq_sum_packet_finrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "_private.ReleaseBoundary.0.PaperIBlock08Tests.mixed_count", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictIdeal_power_mem", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.multiplierNorms", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.monicPrimaryMultiplicityValues_nonempty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.baseChange_nontrivial", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_13", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.proj_packet_self", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualLinearEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "_private.KomorebiVerification.PacketNaturalityCompletion.0.Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1.splitter", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monic_primary_internal_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.quotientAfterEquiv_ker", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.hasCyclicVector_iff_geometricSeedMaximum_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.inj", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.regular_generates_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetQuotientCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.id.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.ctorElimType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.assembleTransferBlockTable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_on_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.BlockModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity.eq_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceNorm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.transferBlock._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_of_commutes", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.seedRank_eq_radicalTop_restricted", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.BlocksSupported", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_9", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.coordinate", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqFormalizationStatus._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.block_intertwining_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localPacketFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum_zero_ne", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packet_sequence_exact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathStep", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.graphEigenMultiplicity._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.heading", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.HasTopologicalSeedRankOne", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.singleOperator_seedNumber_isLeast_of_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedRangeEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.transferBlock.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.zero.elim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.statement", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.transportedUniformity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOps", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_succ", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.eq_iff_projectors_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.maxEigenMultiplicity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.MixedD", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.eq_zero_of_unconditionalNorm_eq_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryGeneratorCount_eq_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportPower", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.coordinateProj_reconstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap_ker_eq_annihilator_of_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.universal_pattern_boundary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.identity._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.boundaryOnly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.transported_locallyConvex", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_module_jacobson", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_14", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathStep_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.hasCyclicVector_iff_seedNumber_eq_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.quotientEmbedding", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply_preserves_reachable_support", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrowWord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_10", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.coordinateProj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.IsCyclic.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.splitter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_zero_val", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.edge_range_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.toPacketObject", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.mem_scalarImage_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.oneBlock_seedRank_eq_ceilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.seedNumber_isLeast_linearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.spectralMultiplicityValues_bddAbove", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_7", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.sum_conditions_comm", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProjectorFamily._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedIndexEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.kernelChecked.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.HasCyclicVector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.abstract_quaternion_presentation", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.splitData._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap_ker", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathAdjacency_mulVec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues_bddAbove", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.algebraTransferEdge_iff_of_bijective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.RadicalTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.local_packetPure_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_faithful", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.logPhase.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketCoordinates._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_range_in_ambient", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_eq_pow", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis_opNorm_le", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.rightStep", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.theoremClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packetMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.corner_one_eq_projector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.operatorAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.finiteSum_limit_bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_le_seedFinrank", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.Packet.fibreLinearProj.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component_le_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.transferBlock_preserves_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_smul", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.lemmaClaim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.kind", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.base_respects", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.conjugateEnd_apply", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_seedNumber_isLeast_two_of_root", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedAction._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component_eq_iff._simp_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.exists_packet_maps_nonzero_comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.qj.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._aux_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "recursor", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_injective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packet.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.DivisionProductModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.maxEigenMultiplicity.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedNumberLE_iff_operatorAlgebra_family", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets._proof_3", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.V", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.ofNat", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_14", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.residueDivisionRing", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.proofTermPresent", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.transferBlock_naturality", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.IntrinsicPrimaryQuotient._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primary_equiv_mem_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.map_packetRange_eq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.finrank_cokernel_eq_finrank_kernel._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_seedCardinality_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.oneBlock_seedFinrank_eq_ceilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitHull_invariant", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_transferBlock_ne_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_prod_productAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetLinearEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebra_mul_eq_blockMul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.linearResidue_finrank", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.recOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftStep", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.CondensationEdge", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.rotation.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packet_spaces_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_19", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetInclusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.packet_nonzero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_eq_charpoly_baseChange_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.HasOneInvariantFactor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportInitial_underlying", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.whole_submodule_packet_exact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.generator.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.exists_leftGenerators_of_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.eigenspace_finrank_pos_iff_mem_spectrum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.seedCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.arrow", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.vertex_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "_private.KomorebiVerification.EllipticAlgorithms.0.Komorebi.FiniteAlgorithms.orbitClosureIter.match_1.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.lemmaClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum_attained", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.infiniteSinglePacket", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.power_kills_of_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbitMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.normalFormToQuotient", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.exactPacketDirectSumCoordinates._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.sourceStatus", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.evalVector._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.TopologicallyCyclic._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.liftActionHom.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.aeval_mem_span_orbit_of_mem", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.path_action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.TransferEdge", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.transferBlock.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.casesOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedClaimKind.default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.support_pattern_algebra_criterion", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprClaimKind", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.right_division_coefficient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks_comp", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.Generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMulClosed_iff_transitive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.original_mem_grouped", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetRange_eq_closure_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Algebra.MatrixSupportMulClosed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualFinite", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.fromModuleHom._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection_range", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localCornerAlgebra._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPackets._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_eq_zero_of_subsingleton", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientInverseAmbient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.support_pattern_invariant", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Polyphase.coeffSection_one_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsicSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.splitter", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis_synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_naturality_package", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugateEnd_eq_zero_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetPure_of_mem_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.no_u_supported_seeds_generate", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instDecidableEqClaimKind._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instBEqFormalizationStatus", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.familyGenerates_iff_polynomialModule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.tensor_endHom_eq_baseChange", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._sunfold", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff._f", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.diagonalApply_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.norm_coordinateOperator_le", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.diagonalizable_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleExistence", "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_semisimple_seed_formula", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.generates_iff_operator_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.coordinateOperator_inverse", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.isClosed_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.grouped_nonzero", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorElim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorLeftTowerInstalled", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.regular_direct_sum_roundtrip", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.one_le_conditionNumber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.sum_localNonzeroSeeds_card_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.recOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.id", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.seedRank_eq_idealTop", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.arrow_natural", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientInverseAmbient", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftTerm", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.y_sq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packet_conditioned_coordinate_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM_toLinearMap", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.eval_comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_length_bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualLinearEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.unique_packet_extension", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.Basic", "name": "KomorebiVerification.sumFirstOddNumbers", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.algebraMap", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr.repr.match_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.OrbitSet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit._simp_1_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn.go", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow_basisFun", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.freeAction._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.strict_seedRank_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.idempotent", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.conjugateEnd.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.isClosed_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.parity_refinement", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.supportedSubmodule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented_respects", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodFstSemilinear._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_regular_multiplicity_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.regular_columns_intertwines", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealToPresented", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.no_reach_into_source", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.operatorHull.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenLabelsFintype._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_length_bound._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.sourceProjection_compression", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupport_mul_left", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassesFintype", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signed_sum_le_norm", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodSndSemilinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.identity._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.summable_coordinate_limit", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_corner", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.oneSeedMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_4", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_16", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor_injective_on_fiber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.packet", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.equation_transport", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countableUnconditionalPacketEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjectorCLM_toLinearMap", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.fineAddress", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.graphSpectrum", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_11", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_natural_rank_one", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds_generate._proof_1_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_3", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instInhabitedClaimRecord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ctorIdx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralFiniteCompletion", "name": "Komorebi.PaperIRelease.GeneralFiniteCompletion.extended_packet_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.algebraZeroAt_iff_of_bijective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.topologicallyCyclic_delta", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.boundedProjector.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.fullMatrix_seedRank_eq_one", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.seed_subset_hull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.empty_vertex_algebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate_proj_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.SixWayCyclicCriterion", "name": "Komorebi.PaperICompletion6.SixWayCyclicCriterion.cyclic_six_way", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.adjoint_transferBlock", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalB.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap_ker", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_6", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_6", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj_apply_ne", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.corollaryClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cyclic_matrix_four_way_iff_of_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientToNormalForm_root", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.normalFormToQuotient_y", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.empty_pattern_boundary", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.paddedBlockSum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.unconditionalNorm_add_le", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.conjectural.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPackets._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedFinrank_isLeast_free_surjection", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Algebra", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.SplitProductAlgebra", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.exists_positive_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockEquivToEnd", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarFactorization", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.span_imageAlgebra_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.packetProjectors._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.seedNumber_isLeast_of_eigenbasis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRightModule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_7", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.difficulty._default", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.dependencySafe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.transported_uniformConstSMul", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.character_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_le_mk_of_familyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.sourceSeed", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.packetCategory._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendedPacketEquivSumQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.seedRank_mono_algebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedRank_eq_spectralSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv_apply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.module", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.swapEnd", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My_sq_eq_Mx_cube_sub_Mx._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.naturalDirectSum_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff._proof_1_2", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.MatrixSupported.add", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenMultiplicity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryQuotientEquivGlobal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.evaluationEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.signedValues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.split._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.continuous", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.packetEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Algebra.matrixSupportMulClosed_iff_transitive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.groupedRange_preserved", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.PureGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.target_coordinate_active_sum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_primaryProduct_equiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basisPacketCoordinate.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupport_mul_right", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter._unsafe_rec", "runtime_only": true }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.queued", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.exists_source_reaching", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.eq_zero_of_unconditionalNorm_eq_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.transported_uniformAddGroup", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "_private.KomorebiVerification.ProjectorCore.0.Komorebi.FiniteDifference.iteratedDiff.match_1.eq_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.phase", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.packetProjection._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.merge_block_naturality", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceIsometry._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.zero_matrix_size_breaks_unguarded_bound", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_fiber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.coordinateOperator._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.ext", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Algebra.MatrixSupported", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.source_vertex_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component_eq_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.absent_factor_contributes_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubalgebra._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.simple_isSimple", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.baseToPresented", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_left", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.numericalOnly.elim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensor_familyGenerates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.corpus", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberMultiplicity_le_of_generates._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.finiteAmplitude_zero", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicSpectrumEquiv", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedIndex_eigenvalue", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.cyclic_annihilator_eq_module_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.nonzero_word_block_strictPath", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.generalSpaceLinearEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetPure_iff_zero_or_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.cyclic_of_label_injective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primaryProduct_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ExactSequences", "name": "Komorebi.PaperIRelease.seedRank_le_add_of_exact", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.transferGraph", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.divisionProduct_seedRank_eq_maxCeilDiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.forwardDiff_neg", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionUniformEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedPresentation._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_10", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.rec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureStep._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualLinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.idempotentRange_eq_closure_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryProduct_mem_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_8", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.classicalInput.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.mappedGeneratedHull_eq_top", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.seedRank_le_of_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.concretePower_apply", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Free", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.recOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetWordSum.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.hasCyclicVector_iff_minpoly_eq_charpoly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.columnsEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.comp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorLeftTower", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertex_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.grammarFromPathRelations", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.algebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_10", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.notes._default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.ctorIdx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.instReprOperatorExpr.repr._sunfold", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.linearIndependent_baseChange_powers", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.sourceSeed.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverWord_preserves_uReachable", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.u_supported_hull_le_uReachable", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedIdealModuleEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodFstSemilinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.seeded_surjection_generates", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_23", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.packet_assembleIn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceLower", "name": "Komorebi.PaperIRelease.localNonzeroSeeds._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow_map_adjacency", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.semisimple_seedRank_of_decompositions", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.toPacketMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.equivalent_norm_packet_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.supportSubmodule._proof_3", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate.eq_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.exists_uniform_bound", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets._simp_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.vertex_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.SeedNumberLE", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.nonzeroIndexFintype._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.finrank_blocks_eq_sum_products", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.packetConditionNumber_eq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.source", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_3", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros_proj_ne_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal_map", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.toContinuousPacketObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientMapCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.ctorElimType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.dualPacketRangeEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertexWord.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealPresentationEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord.match_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.BlockAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.SeedRankBasics.oneSeedMap.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P0_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.dense_free_evaluation", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.irreducible", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.splitter", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.orbit_finrank_eq_minpoly_degree", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonalHom", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.operatorWord.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.seedNumber_one_isLeast_of_cyclic._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.LocalResidue", "name": "Komorebi.PaperICompletion7.LocalResidue.proper_sup_ne_top", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.algorithmClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensor_packet_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocksLinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.exists_divisionProduct_generators_iff_maxCeilDiv_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complex_cycle_seedNumber_isLeast_two", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_lt_aleph0_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.wrong_factor_acts_zero", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.status", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.exists_generating_set_card_eq_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.proofTermPresent.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.SplitProductModule", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketSourceUpper", "name": "Komorebi.PaperIRelease.localPureSeedRank.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word.eq_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.satisfied_symm", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.algebraicHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.conjugate_reachableFrom_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.ofNat_ctorIdx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn.eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.noConfusion", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.packetPureSeedRank_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues_bddAbove", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.InvariantUnder", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2082.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictPath_le_maximal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.toPacketObject", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.fiberColor._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.one_tmul_generates", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.FamilyGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetSupport_image_eq_of_noncancellation", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRight_smul_tmul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.identity._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ctorIdx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.noConfusionType", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.contextOnly.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.theoremClaim", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported.eq_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_12", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.restrictionCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.nonsplit_finite_algebra_api", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquivRange", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.class_strict_path_lengths", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.LeftGenerates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_23", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.qi.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.cyclicMinpolyQuotientEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.annihilator_isTwoSided_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.map_packetRange_eq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.packetClass.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.PrimaryCyclicCriterion", "name": "Komorebi.PaperICompletion6.PrimaryCyclicCriterion.cyclic_of_subsingleton", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.toPacketMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathCombination_action", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyPresentations", "name": "PaperIRelease.TopologyDenseCompletion.restricted_kernel", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.packetSynthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.quotient_basis_lifts_generate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetSupport_image_subset", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.ctorElimType", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.leftTerm.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.underlying._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureBoundaryTests", "name": "Komorebi.PaperIRelease.PureBoundaryTests.singleton_packet_rank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.recOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.volume", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetBlockAlgebraAlgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_noncommutes", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv_intertwines", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.finitely_many_primary_components", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.operator_mem_closedHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.shared_direct_sum_bounds", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.no_strictPath_after_maximal", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.primitiveRoot_ne_inv._proof_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketEquivalentNorm", "name": "Komorebi.PaperIRelease.PacketEquivalentNorm.packetEquivOfEquivalentNorm._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.kernelChecked.sizeOf_spec", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow_left._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.rank_le_card", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprFormalizationStatus", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SemisimpleSeedRank", "name": "Komorebi.SemisimpleSeedRank.LeftGenerates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.sum_fibers", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_primary_membership", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.freeAction_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.blockApply.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coloredSeeds_generate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedProjection.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.residueProj_refinement", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.conditionNumber_symm", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.primary_fiber_presentation_invariant", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.generates_singleton_iff_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.map_mem_span_image_of_intertwining", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.end_finrank_eq_packet_sum_eq_square", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.packet_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.exists_companion_basis_of_cyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates_My", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleSeeds._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreProj_refinement", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.module_smul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.sourcesFintype", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.StrictPath._unsafe_rec", "runtime_only": true }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.mergeAddress._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.seedRank_le_card", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_9", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.idealQuotientMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.intrinsicMultiplicity_X_sub_C_eq_eigenspace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.curveWeight.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_4", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instBEqFormalizationStatus.beq", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj_apply_same", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.onePacket", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.freeAction._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesized_restricted_block", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_quotient_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.pathCombinationWord", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.isClosed_range_of_bounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules_isEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov_apply_eq_zero_of_lt._proof_1_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateInclusion_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_add_val", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusionCLM_toLinearMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.splitProduct_familyGenerates_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.transferBlock_ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedFinrank_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.exists_grouped_primary_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.maxCeilDiv_isLeast_product_generatorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.maxCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.ext", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphReachability", "name": "Komorebi.PaperIRelease.packetGeneratedAlgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.TopologicallyGenerates._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.ScalarQuotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv_apply_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.HasTopologicalSeedRankOne.cardinality_one_and_not_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.multiSeedQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.cyclic_iff_label_injective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.quotientProjector_norm_apply_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packet_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientLiftCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProjectorFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary.eq_def", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.diagonalProjection", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.ceilDiv_isLeast_generatorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.finiteAmplitude.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_baseChange", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "constructor", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "ReleaseBoundary", "name": "Komorebi.PaperICompletion8.DivisionProduct.maxCeilDiv.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.natural_nonzero_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.aeval_apply_of_eigenvector", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.quotientEquiv._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.eq_zero_of_coprime_smul", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorOperator_smul_tmul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularDirectSumEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap._unary._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.complete", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensor_transfer_blocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.packet_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "_private.PaperIRelease.AlgebraTransfer.0.Komorebi.PaperIRelease.packetWordSum.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Operator.lowRankApply.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.concreteBilateralShift_topologicallyCyclic", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operator_seedFinrank_eq_intrinsic_primary_max", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.isClosed_packet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.Supported", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.space_norm_eq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.eq_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.addCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_5", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._proof_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Relation.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.product_familyGenerates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraGeneratedHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralPacketBounds", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.analysis_isBounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.blockMul.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.actionCategory._proof_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis_analysis", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.phase._default", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mixed_product_rank_max_not_sum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.mixedDivision", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily._sizeOf_inst", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.conjectural.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedWeightedDiff_geometric", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.seedRank_eq_maxCeilDiv_of_divisionProduct_decomposition", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.comp._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.transitive_of_mul_closed", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instIsScalarTowerTensorProduct_paperIRelease", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.brecOn.go", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.unitSeed_generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.variableAction._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.hull_empty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.EdgeSurjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.quotient.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power_neg_comp", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.Cyclic.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.action_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_zero_multiplicity", "runtime_only": false }, { "axioms": [ "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientCongr_mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.emptySource", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.twoPackets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_10", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Quantum.diagonalApply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientEquivL._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.proj_diagonalProjection", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.packetPureSeedRank_eq_source_card", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.SeedOperations", "name": "Komorebi.PaperIRelease.SeedOperations.cyclic_annihilator_two_sided_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_height._proof_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_le_succ", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.PureGenerates._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.remarkClaim.elim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_no_reverse", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryUniversal", "name": "Komorebi.PaperIRelease.CategoryExport.transportTerminal", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensor_transfer_blocks._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquivL._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.word._unary._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.collapse._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapsedActionEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.scalarQuotientEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.transferBlock_word", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.boundaryOnly.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.source_block_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorFactorCoordinates", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_le_of_surjective_semilinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.minpoly_natDegree_baseChange", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceBoundary", "name": "Komorebi.PaperIRelease.FiniteDigraph.oneArrow_not_source_boundary", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.OneJordanBlockPerEigenvalue", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv_apply_coe", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.pathStep.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.fullBlockAlgEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.actingOperators", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.definitionClaim.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetSumQuotientMapCLM._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.regularColumnsEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_quotient_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.relationPolynomial_eval_y", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._f", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap_surjective", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedSpace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassesDecidableEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.toTypedData", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.complexCycleRoot", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_12", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjector_bounded", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.endpoint.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.AllGeometricMultiplicitiesOne", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.Sources", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.toModules._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodFstSemilinear._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.presentationCompletion._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.add.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.Index", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.Generates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._simp_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperITransport", "name": "Komorebi.Foundation.LinearProjectorFamily.conjugate._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.Preserves", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedObject.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.summable_finiteSum_bounded", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.arrow", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eV\u2083_mem_ker_arrowB", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.graph_seedNumber_eq_max_eigenspace_multiplicity_of_distinct", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenFibreEquiv._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialModule", "name": "Komorebi.PaperIRelease.PolynomialModule.intrinsic_primary_finite_power_sum", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom._sizeOf_inst", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedAnalysis._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.countable_synthesis_norm_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.ResidueQuotient", "name": "Komorebi.PaperICompletion4.ResidueQuotient.primaryResidueMap_ker", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.operator_seedFinrank_eq_geometricSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.CyclicGeometricCriterion", "name": "Komorebi.PaperICompletion5.CyclicGeometricCriterion.geometricSeedMaximum_eq_one_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Algebra.matrixSupported_one_iff_reflexive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "constructor", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.OneInvariantFactor", "name": "Komorebi.PaperICompletion6.OneInvariantFactor.quotientVectorEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.transferBlock", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotientNormalFormEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.product_normal_form", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.reachPreorder", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.no_strictPath_after_maximal._proof_1_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.topologicalAdd", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.eU\u2081", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrowWord.eq_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.neg.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.fiberProjector.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.singleColumnsEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorActionsCommute", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.synthesize.eq_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.quiverOp_preserves_uReachable._simp_1_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.operator_seedFinrank_eq_primaryGeneratorCount", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderDiagonal_kernel_eq._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.emptyFamily._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryQuotientEquiv._proof_6", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.brecOn", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.primePowerProduct_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.ctorIdx", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.analysis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.delta_dense_span", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.grouped_operatorSupported_iff", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.residueFiberMap.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.brecOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetNormedAddCommGroup", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.action", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.rank_eq_of_continuous_semilinear_equiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._aux_12", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PaperIBlockCompletion", "name": "Komorebi.Foundation.transferBlock_reconstruction_linearMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowB._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.space", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.packetCategory._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_8", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleAdjacency_basisFun._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.actingOperator", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.eigenspace_finrank_eq_zero_of_not_mem_spectrum._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedModuleEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx_eq_multiplication", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.mk", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditionalBridge", "name": "PaperIRelease.TopologyCountablePackets.Projectors.closedPackets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.ctorIdx", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.operator_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.restrictBlocks.eq_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialQuotientEquivCokernel._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extension_unique", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketObject.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "_private.PaperIRelease.GrammarPaths.0.Komorebi.PaperIRelease.GrammarAlgebra.TypedData.pathMap.match_1._arg_pusher", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.idealTopMap_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.coordinateProj.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.range_multiSeedMap", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.Space", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.contextOnly", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.analysis_synthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primarySubmodule_eq_idealPrimary._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.equations", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus._sizeOf_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.liftActionHom._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.missingSeed", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.rightTerm.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.definitionClaim.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.intrinsicMultiplicity_eq_fiber._simp_1_2", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.quotient_root_sq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionRows", "name": "Komorebi.PaperICompletion8.DivisionRows.exists_leftGenerators_of_le", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologySeedRank", "name": "PaperIRelease.TopologyTransport.topologicalSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.coprime_primePower_ideals", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.packetClass", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList_multiplicity_eq_finrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.action_arrow", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphPropagation", "name": "Komorebi.PaperIRelease.EdgeSurjective._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom_surjective", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.packetCornerAlgebra._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.PacketMorphism.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologySemilinearRank", "name": "PaperIRelease.TopologySemilinearRank.generates_image", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.satisfied_refl", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.ProductPresentation", "name": "Komorebi.PaperICompletion8.ProductPresentation.regroupSimpleFactors._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strict_word_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.packetEquiv_apply", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluate", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.PacketCornerCyclic._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA_eU\u2082", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketCorners", "name": "Komorebi.PaperIRelease.cornerCompression._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.descendTo_proj_mkQ", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.graphSpectrum.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.preorderSupportAlgebra", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketLocalRank", "name": "Komorebi.PaperIRelease.localPacketFamily._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.hasCyclicVector_iff_extended_spectral_multiplicities_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.typedArrow._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.packetAddCommGroup._aux_8", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedHom.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.LinearProjectorFamily", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.all_preserve_bot", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.discardZeros._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierFactor_surjective._simp_1_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1_P0_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarIdeal", "name": "Komorebi.PaperIRelease.GrammarAlgebra.presentedToIdeal_quotient", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completedQuotientEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.signed_sum_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraOrbitSet", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.packetInclusionCLM._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.rec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.krylov._unsafe_rec", "runtime_only": true }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Packet.fibreProj_idempotent", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceAddCommGroup._proof_22", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderStrictIdealQuotientEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalA.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.splitter", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.iteratedDiff._unsafe_rec", "runtime_only": true }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.externalInput.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.arrowA.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.hermitian_matrix_seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderQuotientDirectSumEquiv._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleFormula", "name": "Komorebi.PaperICompletion8.SemisimpleFormula.split_radicalTop_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.eigenFibreEquiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprFormalizationStatus.repr", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.Grammar.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.prodSndSemilinear._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.basis_generates_under_operator", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportStarSubalgebra._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.ModuleTop", "name": "Komorebi.PaperICompletion7.ModuleTop.generates_iff_radicalTop", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.tensorRightTowerInstalled", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion4.OperatorIntrinsicFormula", "name": "Komorebi.PaperICompletion4.OperatorIntrinsicFormula.operatorPrimaryComponentEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.strictPath_height", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.spectralList.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.cyclic_iff_top_isPrincipal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packetRangeEquiv._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.seedCategory", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetCoordinateQuotient._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedSynthesis._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.ConditionedCoordinates", "name": "Komorebi.PaperICompletion.ConditionedCoordinates.norm_le_conditionNumber_mul_coordinateOperator", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorRelation.recOn", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopologyGeneral", "name": "Komorebi.PaperIRelease.GeneralPacketTopology.quotientProjectorCLM._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SemisimpleCompletion", "name": "Komorebi.SemisimpleCompletion.exists_splitProduct_generators_iff_maxCeilDiv_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapseFunctor._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.totalR.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "recursor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.rec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_10", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk._flat_ctor", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.KernelAudit", "name": "Komorebi.Verification.fineAddress.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.instModuleTensorProduct_paperIRelease_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instBEqClaimKind.beq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryBoundaries.mergeTwoPackets", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.sequences._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyFiniteCompletion", "name": "PaperIRelease.TopologyFiniteCompletion.extendPacketFamily._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.ofAction._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedPathRelationModuleEquivalence", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyCountablePackets", "name": "PaperIRelease.TopologyCountablePackets.Projectors.mk.inj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.index", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.polynomialCokernelMap._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.map_operatorHull_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.hull_eq_span", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.RegularMultiplicity", "name": "Komorebi.PaperICompletion8.RegularMultiplicity.naturalCopies_seedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.mk.inj", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.instReprFormalizationStatus.repr.match_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion6.ScalarExtension", "name": "Komorebi.PaperICompletion6.ScalarExtension.linearIndependent_baseChange", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraSupport", "name": "Komorebi.PaperIRelease.OperatorSupported", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.definitionClaim", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.blockedByLibrary", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearIsometryEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralNormedPackets", "name": "Komorebi.PaperIRelease.GeneralNormedPackets.ContinuousProjectorFamily.casesOn", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankBasics", "name": "Komorebi.SeedRankBasics.seedRank_linearEquiv", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricMultiplicityValues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.primaryPresentation_nonempty", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyTransport", "name": "PaperIRelease.TopologyTransport.dense_operatorHull_image", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyUnconditional", "name": "PaperIRelease.TopologyUnconditional.ClosedPackets.spaceCompleteSpace", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.LinearPrimaryEigenspace", "name": "Komorebi.PaperICompletion5.LinearPrimaryEigenspace.finrank_cokernel_eq_finrank_kernel", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.restrictTo._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.selfAdjoint_seedRank_eq_max_eigenspace_finrank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.BilateralShiftRepresentation.power", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.TopologyDenseCompletion", "name": "PaperIRelease.TopologyDenseCompletion.completionLinearEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.FiniteAlgorithms.orbitClosureIter_le_orbitHull", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.carrier", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.SpectralCertificates", "name": "Komorebi.PaperICompletion.SpectralCertificates.groupedEigenbasis.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.coefficientCoordinates._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedObject.seeds", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.strictSupportIdeal._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.AlgebraTransferEdge", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.Reach", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Foundation.transferBlock_reconstruction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.comp._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketExactSequence", "name": "Komorebi.Foundation.LinearProjectorFamily.packetInclusion._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketTopology", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientCLM_norm_le_one", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraPreorder", "name": "Komorebi.PaperIRelease.maximalStrictSteps", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraDiagonal", "name": "Komorebi.PaperIRelease.commutes_iff_offdiagonal_zero", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeSynthesis._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.typedCategory._proof_4", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PolynomialMonic", "name": "Komorebi.PaperIRelease.PolynomialModule.monicToSpec_surjective", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.seedRank_imageAlgebra_eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ofModuleIso._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.PrimarySeedFormula", "name": "Komorebi.PaperICompletion3.PrimarySeedFormula.exists_positive_primaryProduct_equiv", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.blockedByLibrary.sizeOf_spec", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.hull_univ", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketAggregation", "name": "Komorebi.PaperIRelease.PacketAggregation.groupedFamily._simp_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.geometricSeedMaximum_eq_spectralSeedMaximum", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.Mx_apply", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketUniversal", "name": "Komorebi.PaperIRelease.PacketUniversal.assembleOut", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycle_root_neighbor_identity._simp_1_7", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion8.DivisionProduct", "name": "Komorebi.PaperICompletion8.DivisionProduct.blockModuleAction", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetPure_mem_range", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.completionEquivOfIsometryDense._proof_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PathGraphKrylov", "name": "Komorebi.PathGraphKrylov.walkMatrix_isUpperTriangular", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.arrow_corner", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryBoundaries", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedRealization.declared", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualLinearEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion5.GeometricSeedFormula", "name": "Komorebi.PaperICompletion5.GeometricSeedFormula.primaryValues_eq_geometricValues", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.classSupport_iff", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimRecord.casesOn", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FiniteDifference.forwardDiff_add", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.positive", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.dualLinearEquiv._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "definition", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.qi", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraQuotient", "name": "Komorebi.PaperIRelease.diagonalClassHom._proof_12", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.FormalizationStatus.blockedByLibrary.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.ofBoundedLinear._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.packetPureSeedRank_le_source_count", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.identity", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.vertex_orthogonal", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.sccDecidableEq", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_7", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.IntrinsicPrimary", "name": "Komorebi.PaperICompletion4.IntrinsicPrimary.primaryToGlobal._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "_private.KomorebiVerification.PacketNaturalityCompletion.0.Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.match_1.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.synthesis._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1_My", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.PacketDescent", "name": "Komorebi.Foundation.LinearProjectorFamily.packetQuotientMap", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.reversed_quaternion_coefficient_fails", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.brecOn.eq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarAlgebra", "name": "Komorebi.PaperIRelease.GrammarAlgebra.CollapsedRealization.casesOn", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "inductive", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.uReachableSubmodule._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.StrictNaturality.StrictSeedMorphism.operator_natural", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.bilateralShift_dense_orbit_of_coordinate_formula", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.proj_other", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Packets.packetPathSum.congr_simp", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.TopologyCategories", "name": "Komorebi.PaperIRelease.TopologyCategories.SeedMorphism.mk.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionObject.mk", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.primaryCongr._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.packetProjection.eq_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.cons.noConfusion", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.My._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPackets.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.BoundedStar", "name": "Komorebi.PaperIRelease.BoundedSupport.supportSubalgebra._proof_8", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.reachPreorder._proof_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.splitActionIso._proof_6", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.imageHull_eq_top", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion.CyclicClassification", "name": "Komorebi.PaperICompletion.CyclicClassification.minpolyQuotientEquivOrbit._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ext", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.orbitFamily", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.sccPartialOrder", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.Reachability.wordApply._sunfold", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.TopologicalCompletion", "name": "KomorebiVerification.TopologicalCompletion.BoundedProjectorFamily.reindexL2LinearEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.algebraMap", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion4.GroupedPrimary", "name": "Komorebi.PaperICompletion4.GroupedPrimary.groupedPrimaryEquiv._proof_1", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.Seed.OperatorExpr.atom.injEq", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarPaths", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedPath.noConfusionType", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceCount", "name": "Komorebi.PaperIRelease.one_le_source_localPureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "constructor", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketObject.mk", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.tensorRight_smul_tmul", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GraphSources", "name": "Komorebi.PaperIRelease.FiniteDigraph.component", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.ext_iff", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketPureRank", "name": "Komorebi.PaperIRelease.seedRank_le_packetPureSeedRank", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "ReleaseBoundary", "name": "PaperIBlock08Tests.quaternion_three_copies_rank_two", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.chosenPrimaryPresentation", "runtime_only": false }, { "axioms": [ "propext" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.evaluateTransported", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.SeedMorphism.mk.injEq", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarEquivalence", "name": "Komorebi.PaperIRelease.GrammarAlgebra.collapse_essSurj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.AlgebraPreorder", "name": "_private.PaperIRelease.AlgebraPreorder.0.Komorebi.PaperIRelease.predecessors_strict_mono", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryPackets", "name": "Komorebi.PaperIRelease.CategoryPackets.PacketMorphism.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.DivisionBlock", "name": "Komorebi.PaperICompletion8.DivisionBlock.block_smul_eq_mul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.PacketBoundaryTests", "name": "Komorebi.PaperIRelease.PacketBoundaryTests.coordinate_swap_cannot_descend", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "KomorebiVerification.ResidueProjectors", "name": "Komorebi.Residue.residueProj", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.seedNumber_isLeast", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.EllipticAlgorithms", "name": "Komorebi.EllipticCoordinates.P1._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": false, "kind": "theorem", "module": "PaperIRelease.CategoryExport", "name": "_private.PaperIRelease.CategoryExport.0.Komorebi.PaperIRelease.CategoryExport.evaluate.match_1.eq_5", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.ExactCoordinates", "name": "Komorebi.Foundation.LinearProjectorFamily.rangeAnalysis_rangeSynthesis", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.CoordinateTransport", "name": "Komorebi.PaperIRelease.CoordinateTransport.packet_rank_invariant", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": false, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "_private.KomorebiVerification.SeedRankOperations.0.Komorebi.SeedRankOperations.seedRank_prod_le_right_of_le", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.TypedQuiver.range_arrowA_third_zero", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GrammarModules", "name": "Komorebi.PaperIRelease.GrammarModules.ActionHom.mk._flat_ctor", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion7.Nakayama", "name": "Komorebi.PaperICompletion7.Nakayama.eq_top_of_sup_ideal_smul", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SingleOperatorGraph", "name": "Komorebi.SingleOperatorGraph.cycleFourierRow._proof_2", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.below", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.GeneralConditionedCoordinates", "name": "Komorebi.PaperIRelease.GeneralConditionedCoordinates.conditionNumber", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperICompletion3.OperatorPrimaryAPI", "name": "Komorebi.PaperICompletion3.OperatorPrimaryAPI.PrimaryPresentation.label", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassSupportEquiv._proof_2", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.PacketNaturalityCompletion", "name": "Komorebi.PacketNaturalityCompletion.FullBlocks.synthesizeBlocks_restrictBlocks", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.AlgebraClassGrouping", "name": "Komorebi.PaperIRelease.preorderClassRangeEquiv", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.FibreRefinement", "name": "Komorebi.Packet.fibreLinearProj._proof_1", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.scalar.elim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GraphSourceProjection", "name": "Komorebi.PaperIRelease.componentProjection_other_packet", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "KomorebiVerification.SeedRankOperations", "name": "Komorebi.SeedRankOperations.productModule._proof_3", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.ScalarExtension", "name": "Komorebi.PaperIRelease.ScalarExtension.tensorRightTower", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.GrammarTyped", "name": "Komorebi.PaperIRelease.GrammarAlgebra.TypedData.vertexOperator.eq_1", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.AlgebraTransfer", "name": "Komorebi.PaperIRelease.packetPure_zero", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "constructor", "module": "KomorebiVerification.ProjectorCore", "name": "Komorebi.ClaimKind.algorithmClaim", "runtime_only": false }, { "axioms": [ "propext", "Classical.choice", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperICompletion8.SemisimpleExistence", "name": "Komorebi.PaperICompletion8.SemisimpleExistence.exists_artinian_radicalTop_seed_formula", "runtime_only": false }, { "axioms": [], "in_project_namespace": true, "kind": "definition", "module": "PaperIRelease.CategoryExport", "name": "Komorebi.PaperIRelease.CategoryExport.Expression.comp.elim", "runtime_only": false }, { "axioms": [ "propext", "Quot.sound" ], "in_project_namespace": true, "kind": "theorem", "module": "PaperIRelease.TensorPackets", "name": "Komorebi.PaperIRelease.tensorPacketRangeEquiv._proof_1", "runtime_only": false } ]