Finite Field
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NPA

依赖分析器

公理浏览器

跟踪形式化证明 registry 中导入的公理，并审计定理依赖。

数学理论以逻辑公理为基础。通过审计反向依赖树，我们可以准确看到哪些定理依赖排中律、选择公理等特定假设。

Eq.rec

来源模块: Mathlib.Algebra.Group.Basic

依赖定理数 13

依赖声明列表
Mathlib.Algebra.Group.Basic.group_conj_slide Mathlib.Algebra.Group.Basic.group_inv_inv Mathlib.Algebra.Group.Basic.group_inv_mul_left_reassoc Mathlib.Algebra.Group.Basic.group_inv_rel_symm_reassoc Mathlib.Algebra.Group.Basic.group_left_cancel Mathlib.Algebra.Group.Basic.group_mul_inv_rev Mathlib.Algebra.Group.Basic.group_product_inv_reassoc Mathlib.Algebra.Group.Basic.group_product_mul_reassoc Mathlib.Algebra.Group.Basic.group_rel_inv_reassoc Mathlib.Algebra.Group.Basic.group_rel_mul_reassoc Mathlib.Algebra.Group.Basic.group_rel_trans_reassoc Mathlib.Algebra.Group.Basic.ker_rel_symm Mathlib.Algebra.Group.Basic.ker_rel_trans

Eq.rec

来源模块: Mathlib.Algebra.Group.Correspondence

依赖定理数 8

依赖声明列表
Mathlib.Algebra.Group.Correspondence.correspondence_containment_evidence Mathlib.Algebra.Group.Correspondence.correspondence_image_subgroup_evidence Mathlib.Algebra.Group.Correspondence.correspondence_image_subgroup_law_args Mathlib.Algebra.Group.Correspondence.correspondence_preimage_subgroup_evidence Mathlib.Algebra.Group.Correspondence.correspondence_preimage_subgroup_law_args Mathlib.Algebra.Group.Correspondence.correspondence_quotient_round_trip_evidence Mathlib.Algebra.Group.Correspondence.correspondence_subgroup_saturation_evidence Mathlib.Algebra.Group.Correspondence.correspondence_theorem_evidence

Eq.rec

来源模块: Mathlib.Algebra.Group.Correspondence.Basic

依赖定理数 16

依赖声明列表
Mathlib.Algebra.Group.Correspondence.Basic.correspondence_group_mul_inv_left_reassoc Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_elim Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_intro Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_inv_closed Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_mul_closed Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_one Mathlib.Algebra.Group.Correspondence.Basic.correspondence_image_preimage_to_quotient Mathlib.Algebra.Group.Correspondence.Basic.correspondence_preimage_contains_normal Mathlib.Algebra.Group.Correspondence.Basic.correspondence_preimage_inv_closed Mathlib.Algebra.Group.Correspondence.Basic.correspondence_preimage_mul_closed Mathlib.Algebra.Group.Correspondence.Basic.correspondence_preimage_one Mathlib.Algebra.Group.Correspondence.Basic.correspondence_quotient_to_image_preimage Mathlib.Algebra.Group.Correspondence.Basic.correspondence_saturation_to_subgroup Mathlib.Algebra.Group.Correspondence.Basic.correspondence_subgroup_saturates Mathlib.Algebra.Group.Correspondence.Basic.correspondence_subgroup_to_preimage_image Mathlib.Algebra.Group.Correspondence.Basic.correspondence_subgroup_to_saturation

Eq.rec

来源模块: Mathlib.Algebra.Group.FirstIsomorphism.Image

依赖定理数 10

依赖声明列表
Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_image_group_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_image_group_facts Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_assoc_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_group_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_inv_mul_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_mul_inv_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_mul_one_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_iso_quotient_one_mul_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_isomorphism_theorem_evidence Mathlib.Algebra.Group.FirstIsomorphism.Image.first_isomorphism_to_image

Eq.rec

来源模块: Mathlib.Algebra.Group.Kernel.Quotient.Group

依赖定理数 7

依赖声明列表
Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_inv_mk Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_inv_mul Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_mul_assoc Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_mul_inv Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_mul_mk Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_mul_one Mathlib.Algebra.Group.Kernel.Quotient.Group.ker_quot_one_mul

Eq.rec

来源模块: Mathlib.Algebra.Group.SecondIsomorphism.Image

依赖定理数 6

依赖声明列表
Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_image_elim Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_image_intro Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_image_to_product_quot Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_product_quot_elim Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_product_quot_intro Mathlib.Algebra.Group.SecondIsomorphism.Image.second_iso_product_quot_to_image

Eq.rec

来源模块: Mathlib.Algebra.Group.Subgroup

依赖定理数 13

依赖声明列表
Mathlib.Algebra.Group.Subgroup.normal_inv_conj_closed Mathlib.Algebra.Group.Subgroup.normal_rel_inv_compat Mathlib.Algebra.Group.Subgroup.normal_rel_mul_compat Mathlib.Algebra.Group.Subgroup.normal_rel_of_eq Mathlib.Algebra.Group.Subgroup.normal_rel_one_of_mem Mathlib.Algebra.Group.Subgroup.normal_rel_one_to_mem Mathlib.Algebra.Group.Subgroup.normal_rel_product_right Mathlib.Algebra.Group.Subgroup.normal_rel_refl Mathlib.Algebra.Group.Subgroup.normal_rel_symm Mathlib.Algebra.Group.Subgroup.normal_rel_trans Mathlib.Algebra.Group.Subgroup.subgroup_product_inv_closed Mathlib.Algebra.Group.Subgroup.subgroup_product_laws Mathlib.Algebra.Group.Subgroup.subgroup_product_mul_closed

Eq.rec

来源模块: Mathlib.Algebra.Group.ThirdIsomorphism

依赖定理数 15

依赖声明列表
Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_conj_closed Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_elim Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_intro Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_inv_closed Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_mul_closed Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_one Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_hn_to_kernel_sound Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_kernel_evidence Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_kernel_intro Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_phi_inv Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_phi_mk Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_phi_mul Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_phi_one Mathlib.Algebra.Group.ThirdIsomorphism.third_iso_phi_surjective Mathlib.Algebra.Group.ThirdIsomorphism.third_isomorphism_theorem_evidence

Eq.rec

来源模块: Mathlib.Algebra.OrderedField.ScalarIdentities

依赖定理数 13

依赖声明列表
Mathlib.Algebra.OrderedField.ScalarIdentities.add_cross_and_sub_cross_cancel_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.add_middle_to_front_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.add_neg_cross_term_to_sub_sum_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.add_pairwise_commute_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.add_sub_cross_cancel_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.cancel_double_zero_term_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.law_of_cosines_scalar_rhs_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.mul_two_neg_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.mul_two_zero_term_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.normalize_add_with_zero_cross_term_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.parallelogram_scalar_rhs_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.polarization_scalar_rhs_from_ring_args Mathlib.Algebra.OrderedField.ScalarIdentities.two_mul_from_ring_args

Eq.rec

来源模块: Mathlib.Algebra.Ring.FirstIsomorphism

依赖定理数 9

依赖声明列表
Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_add Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_hits_image Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_injective Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_mul Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_one Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_surj_image Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_iso_phi_zero Mathlib.Algebra.Ring.FirstIsomorphism.ring_first_isomorphism_to_image Mathlib.Algebra.Ring.FirstIsomorphism.ring_ker_quot_mul_mk

Eq.rec

来源模块: Mathlib.Geometry.Pythagorean

依赖定理数 11

依赖声明列表
Mathlib.Geometry.Pythagorean.dist_sq_law_of_cosines_rhs_from_law_packages Mathlib.Geometry.Pythagorean.law_of_cosines_dist_sq_from_law_packages Mathlib.Geometry.Pythagorean.law_of_cosines_right_angle_specialization Mathlib.Geometry.Pythagorean.law_of_cosines_right_angle_specialization_from_law_packages Mathlib.Geometry.Pythagorean.law_of_cosines_sq_from_law_packages Mathlib.Geometry.Pythagorean.pythagorean_dist_sq_reverse_norm_neg_from_law_packages Mathlib.Geometry.Pythagorean.pythagorean_distance_sq_from_law_packages Mathlib.Geometry.Pythagorean.pythagorean_left_leg_norm_neg_from_law_packages Mathlib.Geometry.Pythagorean.pythagorean_theorem_api_alias Mathlib.Geometry.Pythagorean.pythagorean_theorem_dist_sq Mathlib.Geometry.Pythagorean.pythagorean_theorem_sq

Eq.rec

来源模块: Mathlib.LinearAlgebra.InnerProduct.Derived

依赖定理数 12

依赖声明列表
Mathlib.LinearAlgebra.InnerProduct.Derived.cauchy_schwarz_zero_left_from_law_packages Mathlib.LinearAlgebra.InnerProduct.Derived.cauchy_schwarz_zero_right_from_law_packages Mathlib.LinearAlgebra.InnerProduct.Derived.dot_eq_zero_of_norm_sq_zero_left_from_inner_args Mathlib.LinearAlgebra.InnerProduct.Derived.dot_eq_zero_of_norm_sq_zero_right_from_inner_args Mathlib.LinearAlgebra.InnerProduct.Derived.dot_zero_left_from_law_packages Mathlib.LinearAlgebra.InnerProduct.Derived.dot_zero_right_from_law_packages Mathlib.LinearAlgebra.InnerProduct.Derived.norm_sq_add_neg_left_from_inner_args Mathlib.LinearAlgebra.InnerProduct.Derived.norm_sq_add_of_dot_zero_from_args Mathlib.LinearAlgebra.InnerProduct.Derived.norm_sq_add_of_perp_from_args Mathlib.LinearAlgebra.InnerProduct.Derived.norm_sq_neg_from_inner_args Mathlib.LinearAlgebra.InnerProduct.Derived.parallelogram_law_from_inner_args Mathlib.LinearAlgebra.InnerProduct.Derived.polarization_identity_from_inner_args

Eq.rec

来源模块: Mathlib.Logic.EqReasoning

依赖定理数 11

依赖声明列表
Mathlib.Logic.EqReasoning.eq_calc3 Mathlib.Logic.EqReasoning.eq_cast_trans Mathlib.Logic.EqReasoning.eq_congr2 Mathlib.Logic.EqReasoning.eq_congr_arg Mathlib.Logic.EqReasoning.eq_congr_fun Mathlib.Logic.EqReasoning.eq_rewrite_left Mathlib.Logic.EqReasoning.eq_rewrite_right Mathlib.Logic.EqReasoning.eq_subst Mathlib.Logic.EqReasoning.eq_symm Mathlib.Logic.EqReasoning.eq_trans Mathlib.Logic.EqReasoning.eq_transport_const