PolynomialPrescribedAxiomAudit.lean

1 module
2 public import AffineObstructionCore
3 public import FiniteFiberCounts
4 public import PadicTowerLimit
5 public import PolynomialMinorSelection
6 public import PolynomialPadicContraction
7 public import PolynomialTaylor
8 public import PolynomialTaylorRing
9 public import PolynomialWeightedInverse
10 public import ResidueLiftDigits
11 public import IntegerFiniteCokernel
12 public import PolynomialMotionRational
13 public import PolynomialObstruction
14 public import PolynomialTaylorDisplacement
15 public import PolynomialWeightedNormalization
16 public import PolynomialDigitBridge
17 public import PolynomialMotionEstimate
18 public import PolynomialMotionNormalization
19 public import PolynomialWeightedLift
20 public import PolynomialLiftCounts
21 public import PolynomialRootMotion
22 public import PolynomialSurjectiveStep
23 public import PolynomialIntegerTower
24 public import PolynomialSmoothCounts
25 public import PolynomialTowerControls
26 public import PolynomialPadicLift
27 public import PolynomialCoefficientPerturbation
28 public import PolynomialPadicUnique
29 public import PolynomialParameterSystem
30 public import PolynomialCoordinateReorder
31 public import PolynomialInverseCongruence
32 public import PolynomialLocalSurjective
33 public import PolynomialPrescribedSystem
34 public import PolynomialRootStability
35 public import PolynomialLocalInverse
36 public import PolynomialPrescribedLifts
37 public import PolynomialParameterChart
38 public import PolynomialPrescribedCounts
39 public import PolynomialGeneralChart
40 public import PolynomialPrescribedObstruction
41 public import PolynomialDeformationControls
42 public import PolynomialParameterControls
43 public import PolynomialPrescribedControls
44 public import PolynomialWeightedControls
45 public import PolynomialMotionControls
46 public import PolynomialCoefficientPerturbationContract
47 public import PolynomialGeneralChartContract
48 public import PolynomialHomeomorphContract
49 public import PolynomialLocalMapContract
50 public import PolynomialPadicUniqueContract
51 public import PolynomialPrescribedContract
52 public import PolynomialRootMotionContract
53 public import PolynomialRootStabilityContract
54 public import PolynomialWeightedAuxiliaryContract
55 public import PolynomialWeightedLiftContract
56 @[expose] public section
57 #print axioms Komorebi.FiniteFiberCounts.Fiber
58 #print axioms Komorebi.FiniteFiberCounts.cokernel_card
59 #print axioms Komorebi.FiniteFiberCounts.cokernel_finrank
60 #print axioms Komorebi.FiniteFiberCounts.difference
61 #print axioms Komorebi.FiniteFiberCounts.difference_translate
62 #print axioms Komorebi.FiniteFiberCounts.fiberAddTorsor
63 #print axioms Komorebi.FiniteFiberCounts.fiberEquivKernel
64 #print axioms Komorebi.FiniteFiberCounts.fiber_card
65 #print axioms Komorebi.FiniteFiberCounts.fiber_card_eq_kernel
66 #print axioms Komorebi.FiniteFiberCounts.fiber_card_of_empty
67 #print axioms Komorebi.FiniteFiberCounts.fiber_card_of_nonempty
68 #print axioms Komorebi.FiniteFiberCounts.fiber_nonempty_iff_class_zero
69 #print axioms Komorebi.FiniteFiberCounts.kernel_card
70 #print axioms Komorebi.FiniteFiberCounts.kernel_finrank
71 #print axioms Komorebi.FiniteFiberCounts.rank
72 #print axioms Komorebi.FiniteFiberCounts.translate
73 #print axioms Komorebi.FiniteFiberCounts.translate_add
74 #print axioms Komorebi.FiniteFiberCounts.translate_difference
75 #print axioms Komorebi.FiniteFiberCounts.translate_exists_unique
76 #print axioms Komorebi.FiniteFiberCounts.translate_zero
77 #print axioms Komorebi.IntegerFiniteCokernel.cokernelEquiv
78 #print axioms Komorebi.IntegerFiniteCokernel.cokernelEquiv_mk
79 #print axioms Komorebi.IntegerFiniteCokernel.cokernelEquiv_obstruction
80 #print axioms Komorebi.IntegerFiniteCokernel.cokernel_card_eq
81 #print axioms Komorebi.IntegerFiniteCokernel.digit_range_eq_restrict
82 #print axioms Komorebi.IntegerFiniteCokernel.reduction_surjective
83 #print axioms Komorebi.NativeAffine.Obstruction
84 #print axioms Komorebi.NativeAffine.affine_lift_iff_obstruction_zero
85 #print axioms Komorebi.NativeAffine.affine_residual_transport
86 #print axioms Komorebi.NativeAffine.digitMap
87 #print axioms Komorebi.NativeAffine.finite_affine_obstruction
88 #print axioms Komorebi.NativeAffine.obstruction
89 #print axioms Komorebi.NativeAffine.obstruction_finite
90 #print axioms Komorebi.NativeAffine.obstruction_representative_independent
91 #print axioms Komorebi.NativeAffine.obstruction_zero_iff_correction
92 #print axioms Komorebi.NativeAffine.reduction
93 #print axioms Komorebi.NativeAffine.reduction_zero_iff
94 #print axioms Komorebi.NativeAffine.residual_exists
95 #print axioms Komorebi.NativeAffine.same_residue_iff
96 #print axioms Komorebi.PadicTowerLimit.compatible_int_tower_cauchy
97 #print axioms Komorebi.PadicTowerLimit.compatible_int_tower_limit
98 #print axioms Komorebi.PadicTowerLimit.compatible_int_tower_unique_limit
99 #print axioms Komorebi.PadicTowerLimit.compatible_vector_tower_limit
100 #print axioms Komorebi.PadicTowerLimit.divisible_int_tendsto_zero
101 #print axioms Komorebi.PadicTowerLimit.tower_pair_dvd
102 #print axioms Komorebi.PolynomialCoefficientPerturbation.digitJacobian_perturb_eq
103 #print axioms Komorebi.PolynomialCoefficientPerturbation.digitJacobian_perturb_point_eq
104 #print axioms Komorebi.PolynomialCoefficientPerturbation.evalSystem_perturb
105 #print axioms Komorebi.PolynomialCoefficientPerturbation.exists_padic_root_perturb
106 #print axioms Komorebi.PolynomialCoefficientPerturbation.exists_padic_root_power_perturb
107 #print axioms Komorebi.PolynomialCoefficientPerturbation.lower_root_perturb
108 #print axioms Komorebi.PolynomialCoefficientPerturbation.padicEval_perturb
109 #print axioms Komorebi.PolynomialCoefficientPerturbation.pderiv_perturb
110 #print axioms Komorebi.PolynomialCoefficientPerturbation.perturb
111 #print axioms Komorebi.PolynomialCoefficientPerturbationContract.explicit_perturbed_jacobian
112 #print axioms Komorebi.PolynomialCoefficientPerturbationContract.explicit_power_perturbation_root
113 #print axioms Komorebi.PolynomialCoordinateReorder.continuous_reorderPoint
114 #print axioms Komorebi.PolynomialCoordinateReorder.digitJacobian_single
115 #print axioms Komorebi.PolynomialCoordinateReorder.evalSystem_reorder
116 #print axioms Komorebi.PolynomialCoordinateReorder.evalSystem_reorder_at
117 #print axioms Komorebi.PolynomialCoordinateReorder.exists_reorder_solvedJacobian_surjective
118 #print axioms Komorebi.PolynomialCoordinateReorder.padicEval_reorder
119 #print axioms Komorebi.PolynomialCoordinateReorder.padicEval_reorder_at
120 #print axioms Komorebi.PolynomialCoordinateReorder.pderiv_eval_reorder
121 #print axioms Komorebi.PolynomialCoordinateReorder.pderiv_reorder
122 #print axioms Komorebi.PolynomialCoordinateReorder.reorderPoint
123 #print axioms Komorebi.PolynomialCoordinateReorder.reorderPoint_inverse
124 #print axioms Komorebi.PolynomialCoordinateReorder.reorderPoint_inverse'
125 #print axioms Komorebi.PolynomialCoordinateReorder.reorderSystem
126 #print axioms Komorebi.PolynomialCoordinateReorder.solvedJacobian_reorder_apply
127 #print axioms Komorebi.PolynomialDeformationControls.linear_shift_coefficient_perturbation
128 #print axioms Komorebi.PolynomialDeformationControls.linear_shift_no_extra_padic_precision
129 #print axioms Komorebi.PolynomialDeformationControls.squareMinusOne
130 #print axioms Komorebi.PolynomialDeformationControls.square_minus_one_jacobian_bijective
131 #print axioms Komorebi.PolynomialDeformationControls.square_minus_one_not_global_unique
132 #print axioms Komorebi.PolynomialDeformationControls.square_minus_one_two_padic_roots
133 #print axioms Komorebi.PolynomialDigitBridge.DigitSolutions
134 #print axioms Komorebi.PolynomialDigitBridge.digitJacobian
135 #print axioms Komorebi.PolynomialDigitBridge.digit_solution_iff
136 #print axioms Komorebi.PolynomialDigitBridge.digit_solutions_nonempty_iff
137 #print axioms Komorebi.PolynomialDigitBridge.integerLift
138 #print axioms Komorebi.PolynomialDigitBridge.reduction_integerLift
139 #print axioms Komorebi.PolynomialDigitBridge.reduction_jacobian
140 #print axioms Komorebi.PolynomialGeneralChart.exists_parameter_homeomorph
141 #print axioms Komorebi.PolynomialGeneralChart.reorderRootHomeomorph
142 #print axioms Komorebi.PolynomialGeneralChartContract.full_rectangular_chart
143 #print axioms Komorebi.PolynomialHomeomorphContract.square_homeomorphism
144 #print axioms Komorebi.PolynomialIntegerTower.exists_compatible_tower
145 #print axioms Komorebi.PolynomialIntegerTower.exists_compatible_tower_strong
146 #print axioms Komorebi.PolynomialIntegerTower.tower_digitJacobian_eq
147 #print axioms Komorebi.PolynomialIntegerTower.tower_initial_congruent
148 #print axioms Komorebi.PolynomialIntegerTower.tower_pairwise_congruent
149 #print axioms Komorebi.PolynomialInverseCongruence.integer_inverse_congruence
150 #print axioms Komorebi.PolynomialInverseCongruence.integer_inverse_congruence_step
151 #print axioms Komorebi.PolynomialInverseCongruence.padicEval_congruent
152 #print axioms Komorebi.PolynomialInverseCongruence.padic_congruence_iff
153 #print axioms Komorebi.PolynomialInverseCongruence.padic_inverse_congruence
154 #print axioms Komorebi.PolynomialInverseCongruence.padic_map_injective
155 #print axioms Komorebi.PolynomialLiftCounts.ActualLifts
156 #print axioms Komorebi.PolynomialLiftCounts.digitAddTorsor
157 #print axioms Komorebi.PolynomialLiftCounts.digitEquivLifts
158 #print axioms Komorebi.PolynomialLiftCounts.digit_residue_solution_iff
159 #print axioms Komorebi.PolynomialLiftCounts.finite_polynomial_lift_count
160 #print axioms Komorebi.PolynomialLiftCounts.liftEquivKernel
161 #print axioms Komorebi.PolynomialLiftCounts.lift_card
162 #print axioms Komorebi.PolynomialLiftCounts.obstructionEquiv
163 #print axioms Komorebi.PolynomialLiftCounts.obstructionEquiv_class
164 #print axioms Komorebi.PolynomialLiftCounts.obstruction_card
165 #print axioms Komorebi.PolynomialLocalInverse.ballMap
166 #print axioms Komorebi.PolynomialLocalInverse.ballMap_bijective
167 #print axioms Komorebi.PolynomialLocalInverse.continuous_ballMap
168 #print axioms Komorebi.PolynomialLocalInverse.localHomeomorph
169 #print axioms Komorebi.PolynomialLocalInverse.localHomeomorph_apply
170 #print axioms Komorebi.PolynomialLocalInverse.localHomeomorph_symm_congruent
171 #print axioms Komorebi.PolynomialLocalInverse.localHomeomorph_symm_eval
172 #print axioms Komorebi.PolynomialLocalMapContract.all_depths_reflected
173 #print axioms Komorebi.PolynomialLocalMapContract.arbitrary_padic_target
174 #print axioms Komorebi.PolynomialLocalSurjective.digitJacobian_sub_C
175 #print axioms Komorebi.PolynomialLocalSurjective.exists_integer_target_preimage
176 #print axioms Komorebi.PolynomialLocalSurjective.exists_padic_preimage
177 #print axioms Komorebi.PolynomialLocalSurjective.isClosed_residueBall
178 #print axioms Komorebi.PolynomialLocalSurjective.isCompact_residueBall
179 #print axioms Komorebi.PolynomialLocalSurjective.residueBall
180 #print axioms Komorebi.PolynomialLocalSurjective.truncInt_tendsto
181 #print axioms Komorebi.PolynomialMinorSelection.exists_permuted_columns
182 #print axioms Komorebi.PolynomialMinorSelection.exists_prime_permuted_columns
183 #print axioms Komorebi.PolynomialMinorSelection.exists_selected_columns
184 #print axioms Komorebi.PolynomialMotionControls.exists_sharp_motion_root
185 #print axioms Komorebi.PolynomialMotionControls.no_uniform_extra_error_digit
186 #print axioms Komorebi.PolynomialMotionControls.sharpQuadratic
187 #print axioms Komorebi.PolynomialMotionControls.sharpQuadratic_base
188 #print axioms Komorebi.PolynomialMotionControls.sharp_error_of_even_root
189 #print axioms Komorebi.PolynomialMotionControls.sharp_mod_eight
190 #print axioms Komorebi.PolynomialMotionEstimate.first_order_error_dvd
191 #print axioms Komorebi.PolynomialMotionNormalization.eval_perturbSystem
192 #print axioms Komorebi.PolynomialMotionNormalization.exists_eval_scaled_difference
193 #print axioms Komorebi.PolynomialMotionNormalization.exists_motion_normalization
194 #print axioms Komorebi.PolynomialMotionNormalization.perturbSystem
195 #print axioms Komorebi.PolynomialMotionNormalization.precondition_perturbSystem
196 #print axioms Komorebi.PolynomialMotionRational.coe_mulVec
197 #print axioms Komorebi.PolynomialMotionRational.exists_rational_error
198 #print axioms Komorebi.PolynomialMotionRational.scaled_inverse_mulVec
199 #print axioms Komorebi.PolynomialObstruction.dvd_iff_of_dvd_sub
200 #print axioms Komorebi.PolynomialObstruction.evalSystem
201 #print axioms Komorebi.PolynomialObstruction.evalSystem_apply
202 #print axioms Komorebi.PolynomialObstruction.finite_polynomial_obstruction
203 #print axioms Komorebi.PolynomialObstruction.jacobian
204 #print axioms Komorebi.PolynomialObstruction.jacobian_apply
205 #print axioms Komorebi.PolynomialObstruction.next_level_iff_digit
206 #print axioms Komorebi.PolynomialObstruction.polynomial_lift_iff_obstruction_zero
207 #print axioms Komorebi.PolynomialObstruction.polynomial_same_residue_lift_iff
208 #print axioms Komorebi.PolynomialObstruction.residual_exists
209 #print axioms Komorebi.PolynomialObstruction.residual_unique
210 #print axioms Komorebi.PolynomialObstruction.taylor_residual_dvd
211 #print axioms Komorebi.PolynomialPadicContraction.contracting_contractionMap
212 #print axioms Komorebi.PolynomialPadicContraction.contractionMap
213 #print axioms Komorebi.PolynomialPadicContraction.evalSystem
214 #print axioms Komorebi.PolynomialPadicContraction.eval_dist_le
215 #print axioms Komorebi.PolynomialPadicContraction.eval_dvd_of_dvd
216 #print axioms Komorebi.PolynomialPadicContraction.exists_unique_fixedPoint
217 #print axioms Komorebi.PolynomialPadicContraction.exists_unique_fixedPoint_divisible
218 #print axioms Komorebi.PolynomialPadicContraction.fixedPoint_divisible
219 #print axioms Komorebi.PolynomialPadicContraction.lipschitz_evalSystem
220 #print axioms Komorebi.PolynomialPadicLift.continuous_padicEval
221 #print axioms Komorebi.PolynomialPadicLift.exists_padic_root
222 #print axioms Komorebi.PolynomialPadicLift.exists_padic_root_with_tower
223 #print axioms Komorebi.PolynomialPadicLift.padicEval
224 #print axioms Komorebi.PolynomialPadicLift.padicEval_intCast
225 #print axioms Komorebi.PolynomialPadicLift.polynomial_tower_limit_root
226 #print axioms Komorebi.PolynomialPadicUnique.exists_unique_padic_root
227 #print axioms Komorebi.PolynomialPadicUnique.int_pow_dvd_iff
228 #print axioms Komorebi.PolynomialPadicUnique.padic_root_unique
229 #print axioms Komorebi.PolynomialPadicUnique.rootResidueLift
230 #print axioms Komorebi.PolynomialPadicUnique.root_next_residue_eq
231 #print axioms Komorebi.PolynomialPadicUnique.toZModPow_eq_iff_dvd_sub
232 #print axioms Komorebi.PolynomialPadicUnique.truncInt
233 #print axioms Komorebi.PolynomialPadicUnique.truncInt_eval_residue
234 #print axioms Komorebi.PolynomialPadicUnique.truncInt_precision
235 #print axioms Komorebi.PolynomialPadicUnique.truncInt_root
236 #print axioms Komorebi.PolynomialPadicUniqueContract.explicit_arbitrary_root_uniqueness
237 #print axioms Komorebi.PolynomialPadicUniqueContract.explicit_unique_padic_root
238 #print axioms Komorebi.PolynomialParameterChart.chartGraph_iff
239 #print axioms Komorebi.PolynomialParameterChart.chartPhi
240 #print axioms Komorebi.PolynomialParameterChart.chartPoint
241 #print axioms Komorebi.PolynomialParameterChart.chartPoint_congruent
242 #print axioms Komorebi.PolynomialParameterChart.chartPoint_congruent_iff
243 #print axioms Komorebi.PolynomialParameterChart.chartPoint_free
244 #print axioms Komorebi.PolynomialParameterChart.chartPoint_graph
245 #print axioms Komorebi.PolynomialParameterChart.chartPoint_root
246 #print axioms Komorebi.PolynomialParameterChart.chartPoint_spec
247 #print axioms Komorebi.PolynomialParameterChart.chartPoint_unique
248 #print axioms Komorebi.PolynomialParameterChart.chartTarget
249 #print axioms Komorebi.PolynomialParameterChart.continuous_chartPhi
250 #print axioms Komorebi.PolynomialParameterChart.continuous_chartPoint
251 #print axioms Komorebi.PolynomialParameterChart.continuous_chartTarget
252 #print axioms Komorebi.PolynomialParameterChart.parameterHomeomorph
253 #print axioms Komorebi.PolynomialParameterControls.full_jacobian_surjective
254 #print axioms Komorebi.PolynomialParameterControls.no_root_at_parameter_two
255 #print axioms Komorebi.PolynomialParameterControls.parameter_two_near_origin
256 #print axioms Komorebi.PolynomialParameterControls.solved_jacobian_not_surjective
257 #print axioms Komorebi.PolynomialParameterControls.solved_jacobian_zero
258 #print axioms Komorebi.PolynomialParameterControls.squareMinusParameter
259 #print axioms Komorebi.PolynomialParameterSystem.augmented
260 #print axioms Komorebi.PolynomialParameterSystem.augmented_free
261 #print axioms Komorebi.PolynomialParameterSystem.augmented_jacobian_surjective
262 #print axioms Komorebi.PolynomialParameterSystem.augmented_solved
263 #print axioms Komorebi.PolynomialParameterSystem.continuous_freePart
264 #print axioms Komorebi.PolynomialParameterSystem.continuous_join
265 #print axioms Komorebi.PolynomialParameterSystem.continuous_solvedPart
266 #print axioms Komorebi.PolynomialParameterSystem.digitJacobian_augmented
267 #print axioms Komorebi.PolynomialParameterSystem.digitJacobian_join_zero
268 #print axioms Komorebi.PolynomialParameterSystem.evalSystem_augmented
269 #print axioms Komorebi.PolynomialParameterSystem.freePart
270 #print axioms Komorebi.PolynomialParameterSystem.freePart_join
271 #print axioms Komorebi.PolynomialParameterSystem.join
272 #print axioms Komorebi.PolynomialParameterSystem.join_free
273 #print axioms Komorebi.PolynomialParameterSystem.join_parts
274 #print axioms Komorebi.PolynomialParameterSystem.join_solved
275 #print axioms Komorebi.PolynomialParameterSystem.padicEval_augmented
276 #print axioms Komorebi.PolynomialParameterSystem.padicEval_augmented_iff
277 #print axioms Komorebi.PolynomialParameterSystem.solvedJacobian
278 #print axioms Komorebi.PolynomialParameterSystem.solvedPart
279 #print axioms Komorebi.PolynomialParameterSystem.solvedPart_join
280 #print axioms Komorebi.PolynomialPrescribedContract.ActualResidues
281 #print axioms Komorebi.PolynomialPrescribedContract.actualResidueEquiv
282 #print axioms Komorebi.PolynomialPrescribedContract.actualSolvedMap
283 #print axioms Komorebi.PolynomialPrescribedContract.actual_lower_root_obstruction
284 #print axioms Komorebi.PolynomialPrescribedContract.actual_lower_root_prime_count
285 #print axioms Komorebi.PolynomialPrescribedControls.digit_one_empty
286 #print axioms Komorebi.PolynomialPrescribedControls.digit_one_for_three_empty
287 #print axioms Komorebi.PolynomialPrescribedControls.digit_two_for_three_exists
288 #print axioms Komorebi.PolynomialPrescribedControls.full_jacobian_surjective
289 #print axioms Komorebi.PolynomialPrescribedControls.parameterOnly
290 #print axioms Komorebi.PolynomialPrescribedControls.parameterPlusThree
291 #print axioms Komorebi.PolynomialPrescribedControls.prescribed_one_for_three_no_actual_lift
292 #print axioms Komorebi.PolynomialPrescribedControls.prescribed_one_no_actual_lift
293 #print axioms Komorebi.PolynomialPrescribedControls.prescribed_two_for_three_actual_lift
294 #print axioms Komorebi.PolynomialPrescribedControls.prescribed_zero_actual_card
295 #print axioms Komorebi.PolynomialPrescribedControls.solved_jacobian_zero
296 #print axioms Komorebi.PolynomialPrescribedControls.three_residual
297 #print axioms Komorebi.PolynomialPrescribedControls.zeroDigitEquiv
298 #print axioms Komorebi.PolynomialPrescribedControls.zero_digit_card
299 #print axioms Komorebi.PolynomialPrescribedControls.zero_residual
300 #print axioms Komorebi.PolynomialPrescribedCounts.digitAddTorsor
301 #print axioms Komorebi.PolynomialPrescribedCounts.digit_card
302 #print axioms Komorebi.PolynomialPrescribedCounts.liftAddTorsor
303 #print axioms Komorebi.PolynomialPrescribedCounts.liftEquivKernel
304 #print axioms Komorebi.PolynomialPrescribedCounts.lift_card
305 #print axioms Komorebi.PolynomialPrescribedCounts.lift_card_eq_kernel
306 #print axioms Komorebi.PolynomialPrescribedCounts.obstruction_card
307 #print axioms Komorebi.PolynomialPrescribedCounts.obstruction_finrank
308 #print axioms Komorebi.PolynomialPrescribedLifts.PrescribedLifts
309 #print axioms Komorebi.PolynomialPrescribedLifts.freePart_digitResidue
310 #print axioms Komorebi.PolynomialPrescribedLifts.prescribedDigitEquivLifts
311 #print axioms Komorebi.PolynomialPrescribedLifts.prescribedDigitEquivLifts_apply
312 #print axioms Komorebi.PolynomialPrescribedLifts.prescribedDigitEquivRestricted
313 #print axioms Komorebi.PolynomialPrescribedLifts.restrictedDigitEquivLifts
314 #print axioms Komorebi.PolynomialPrescribedObstruction.finite_prescribed_lift_count
315 #print axioms Komorebi.PolynomialPrescribedObstruction.finite_prescribed_obstruction
316 #print axioms Komorebi.PolynomialPrescribedObstruction.prescribed_lift_iff_obstruction_zero
317 #print axioms Komorebi.PolynomialPrescribedObstruction.prescribed_obstruction_finite
318 #print axioms Komorebi.PolynomialPrescribedObstruction.prescribed_residue_exists_iff
319 #print axioms Komorebi.PolynomialPrescribedSystem.PrescribedDigits
320 #print axioms Komorebi.PolynomialPrescribedSystem.PrescribedObstruction
321 #print axioms Komorebi.PolynomialPrescribedSystem.digitJacobian_join
322 #print axioms Komorebi.PolynomialPrescribedSystem.obstruction
323 #print axioms Komorebi.PolynomialPrescribedSystem.parameterJacobian
324 #print axioms Komorebi.PolynomialPrescribedSystem.parameterResidual
325 #print axioms Komorebi.PolynomialPrescribedSystem.prescribed_digits_finite
326 #print axioms Komorebi.PolynomialPrescribedSystem.prescribed_digits_nonempty_iff
327 #print axioms Komorebi.PolynomialPrescribedSystem.prescribed_equation_iff
328 #print axioms Komorebi.PolynomialPrescribedSystem.solvedJacobian
329 #print axioms Komorebi.PolynomialRootMotion.exists_perturbed_root_certificate
330 #print axioms Komorebi.PolynomialRootMotion.exists_root_from_original_preconditioner
331 #print axioms Komorebi.PolynomialRootMotion.exists_root_motion
332 #print axioms Komorebi.PolynomialRootMotion.exists_unique_root_motion
333 #print axioms Komorebi.PolynomialRootMotionContract.original_jacobian_integral_error
334 #print axioms Komorebi.PolynomialRootMotionContract.original_jacobian_rational_motion
335 #print axioms Komorebi.PolynomialRootStability.exists_nearby_perturbed_root
336 #print axioms Komorebi.PolynomialRootStability.exists_root_and_unique_perturbation
337 #print axioms Komorebi.PolynomialRootStability.exists_unique_nearby_perturbed_root
338 #print axioms Komorebi.PolynomialRootStability.integer_congruent_of_common_padic
339 #print axioms Komorebi.PolynomialRootStability.perturbed_roots_congruent
340 #print axioms Komorebi.PolynomialRootStabilityContract.explicit_lower_root_and_unique_perturbation
341 #print axioms Komorebi.PolynomialRootStabilityContract.explicit_rectangular_nearby_root
342 #print axioms Komorebi.PolynomialRootStabilityContract.explicit_square_root_displacement
343 #print axioms Komorebi.PolynomialSmoothCounts.exists_regular_tower
344 #print axioms Komorebi.PolynomialSmoothCounts.smooth_dimension
345 #print axioms Komorebi.PolynomialSmoothCounts.smooth_lift_card
346 #print axioms Komorebi.PolynomialSmoothCounts.smooth_obstruction_card
347 #print axioms Komorebi.PolynomialSmoothCounts.smooth_rank
348 #print axioms Komorebi.PolynomialSurjectiveStep.digitJacobian_eq
349 #print axioms Komorebi.PolynomialSurjectiveStep.digitJacobian_shift_eq
350 #print axioms Komorebi.PolynomialSurjectiveStep.one_step_lift
351 #print axioms Komorebi.PolynomialTaylor.directional
352 #print axioms Komorebi.PolynomialTaylor.directional_C
353 #print axioms Komorebi.PolynomialTaylor.directional_X
354 #print axioms Komorebi.PolynomialTaylor.directional_add
355 #print axioms Komorebi.PolynomialTaylor.directional_mul
356 #print axioms Komorebi.PolynomialTaylor.eval_dvd_of_dvd
357 #print axioms Komorebi.PolynomialTaylor.pderiv_eval_dvd_of_dvd
358 #print axioms Komorebi.PolynomialTaylor.taylor_dvd
359 #print axioms Komorebi.PolynomialTaylor.taylor_step_dvd
360 #print axioms Komorebi.PolynomialTaylorDisplacement.taylor_remainder_dvd
361 #print axioms Komorebi.PolynomialTaylorRing.eval_dvd_of_dvd
362 #print axioms Komorebi.PolynomialTaylorRing.eval_linearPart
363 #print axioms Komorebi.PolynomialTaylorRing.eval_scaled_bind
364 #print axioms Komorebi.PolynomialTaylorRing.eval_zero_linearPart
365 #print axioms Komorebi.PolynomialTaylorRing.exists_eval_scaled_remainder
366 #print axioms Komorebi.PolynomialTaylorRing.exists_scaled_remainder
367 #print axioms Komorebi.PolynomialTaylorRing.linearPart
368 #print axioms Komorebi.PolynomialTaylorRing.linearPart_C
369 #print axioms Komorebi.PolynomialTaylorRing.linearPart_X
370 #print axioms Komorebi.PolynomialTaylorRing.linearPart_add
371 #print axioms Komorebi.PolynomialTaylorRing.linearPart_mul
372 #print axioms Komorebi.PolynomialTowerControls.linearMinusTwo
373 #print axioms Komorebi.PolynomialTowerControls.linear_shift_no_extra_precision
374 #print axioms Komorebi.PolynomialTowerControls.linear_shift_nonsingular_lower_root
375 #print axioms Komorebi.PolynomialTowerControls.projectionSystem
376 #print axioms Komorebi.PolynomialTowerControls.projection_jacobian_surjective
377 #print axioms Komorebi.PolynomialTowerControls.projection_two_padic_roots
378 #print axioms Komorebi.PolynomialTowerControls.squareMinusFive
379 #print axioms Komorebi.PolynomialTowerControls.square_minus_five_lower_steps
380 #print axioms Komorebi.PolynomialTowerControls.square_minus_five_no_mod_eight
381 #print axioms Komorebi.PolynomialTowerControls.square_minus_five_no_tower
382 #print axioms Komorebi.PolynomialWeightedAuxiliaryContract.actual_polynomial_contraction
383 #print axioms Komorebi.PolynomialWeightedAuxiliaryContract.exact_inverse_denominator_certificate
384 #print axioms Komorebi.PolynomialWeightedAuxiliaryContract.uniform_polynomial_taylor
385 #print axioms Komorebi.PolynomialWeightedControls.boundary_exact_residual_depth
386 #print axioms Komorebi.PolynomialWeightedControls.boundary_no_mod_eight
387 #print axioms Komorebi.PolynomialWeightedControls.boundary_no_padic_root
388 #print axioms Komorebi.PolynomialWeightedControls.boundary_no_root
389 #print axioms Komorebi.PolynomialWeightedControls.boundary_residual_derivative
390 #print axioms Komorebi.PolynomialWeightedControls.boundary_scaled_inverse
391 #print axioms Komorebi.PolynomialWeightedControls.linear_displacement_sharp
392 #print axioms Komorebi.PolynomialWeightedControls.linear_perturbation_root
393 #print axioms Komorebi.PolynomialWeightedControls.prime_power_exact_depth
394 #print axioms Komorebi.PolynomialWeightedControls.squarePlusThree
395 #print axioms Komorebi.PolynomialWeightedControls.weightedLinear
396 #print axioms Komorebi.PolynomialWeightedInverse.bounded_inverse_iff_certificate
397 #print axioms Komorebi.PolynomialWeightedInverse.certificate_of_integral_inverse
398 #print axioms Komorebi.PolynomialWeightedInverse.eval_precondition
399 #print axioms Komorebi.PolynomialWeightedInverse.integral_inverse_iff_certificate
400 #print axioms Komorebi.PolynomialWeightedInverse.integral_inverse_of_certificate
401 #print axioms Komorebi.PolynomialWeightedInverse.jacobian
402 #print axioms Komorebi.PolynomialWeightedInverse.jacobian_precondition
403 #print axioms Komorebi.PolynomialWeightedInverse.mulVec_injective_of_scalar_certificate
404 #print axioms Komorebi.PolynomialWeightedInverse.mulVec_preserves_dvd
405 #print axioms Komorebi.PolynomialWeightedInverse.padic_mulVec_injective
406 #print axioms Komorebi.PolynomialWeightedInverse.precondition
407 #print axioms Komorebi.PolynomialWeightedInverse.precondition_root_iff
408 #print axioms Komorebi.PolynomialWeightedInverse.rationalMatrix
409 #print axioms Komorebi.PolynomialWeightedInverse.rationalMatrix_injective
410 #print axioms Komorebi.PolynomialWeightedInverse.rationalMatrix_isUnit_of_certificate
411 #print axioms Komorebi.PolynomialWeightedInverse.rationalMatrix_mul
412 #print axioms Komorebi.PolynomialWeightedInverse.rationalMatrix_scalar
413 #print axioms Komorebi.PolynomialWeightedLift.exists_root_of_normalization
414 #print axioms Komorebi.PolynomialWeightedLift.exists_unique_weighted_root
415 #print axioms Komorebi.PolynomialWeightedLift.exists_weighted_root
416 #print axioms Komorebi.PolynomialWeightedLift.exists_weighted_root_certificate
417 #print axioms Komorebi.PolynomialWeightedLift.shiftedPoint
418 #print axioms Komorebi.PolynomialWeightedLiftContract.actual_jacobian_bounded_inverse
419 #print axioms Komorebi.PolynomialWeightedLiftContract.actual_jacobian_integral_certificate
420 #print axioms Komorebi.PolynomialWeightedNormalization.exists_normalization
421 #print axioms Komorebi.PolynomialWeightedNormalization.precondition_directional
422 #print axioms Komorebi.ResidueLiftDigits.ResidueFiber
423 #print axioms Komorebi.ResidueLiftDigits.digitEquivResidue
424 #print axioms Komorebi.ResidueLiftDigits.digitEquivResidue_apply
425 #print axioms Komorebi.ResidueLiftDigits.digitResidue
426 #print axioms Komorebi.ResidueLiftDigits.digitResidue_injective
427 #print axioms Komorebi.ResidueLiftDigits.digitResidue_mem
428 #print axioms Komorebi.ResidueLiftDigits.digitResidue_surjective
429 #print axioms Komorebi.ResidueLiftDigits.next_modulus_dvd_val_sub_shift
430 #print axioms Komorebi.ResidueLiftDigits.residueFiber_card
431 #print axioms Komorebi.ResidueLiftDigits.shift_cast_eq_iff

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