Finite Field
30-sec diagnosis
NPA

Dependency Analyzer

Axioms Explorer

Track which axioms are imported across the formal proof registry and audit theorem dependencies.

Mathematical theories assume logical axioms as their foundation. By auditing the reverse dependency tree, we can see exactly which theorems rely on specific assumptions like the law of excluded middle or the axiom of choice.

Eq.rec

Origin Module: Mathlib.Algebra.Group.Basic

Dependent Theorems 13

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.Correspondence

Dependent Theorems 8

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.Correspondence.Basic

Dependent Theorems 16

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.FirstIsomorphism.Image

Dependent Theorems 10

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.Kernel.Quotient.Group

Dependent Theorems 7

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.Quotient.Group

Dependent Theorems 7

Dependent Declarations List
Mathlib.Algebra.Group.Quotient.Group.normal_quot_inv_mk Mathlib.Algebra.Group.Quotient.Group.normal_quot_inv_mul Mathlib.Algebra.Group.Quotient.Group.normal_quot_mul_assoc Mathlib.Algebra.Group.Quotient.Group.normal_quot_mul_inv Mathlib.Algebra.Group.Quotient.Group.normal_quot_mul_mk Mathlib.Algebra.Group.Quotient.Group.normal_quot_mul_one Mathlib.Algebra.Group.Quotient.Group.normal_quot_one_mul

Eq.rec

Origin Module: Mathlib.Algebra.Group.SecondIsomorphism.Image

Dependent Theorems 6

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.Subgroup

Dependent Theorems 13

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Group.ThirdIsomorphism

Dependent Theorems 15

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.OrderedField.ScalarIdentities

Dependent Theorems 13

Dependent Declarations List
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

Origin Module: Mathlib.Algebra.Ring.FirstIsomorphism

Dependent Theorems 9

Dependent Declarations List
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

Origin Module: Mathlib.Geometry.Pythagorean

Dependent Theorems 11

Dependent Declarations List
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

Origin Module: Mathlib.LinearAlgebra.InnerProduct.Derived

Dependent Theorems 12

Dependent Declarations List
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

Origin Module: Mathlib.Logic.EqReasoning

Dependent Theorems 11

Dependent Declarations List
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