file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Data/Fin/VecNotation.lean | Matrix.vecAppend_apply_zero | [] | [
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_mul' | [
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Mathlib/Data/Set/Image.lean | Set.coe_comp_rangeFactorization | [] | [
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40
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_const | [
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.norm_setToL1S_le | [
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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix_comp | [
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Mathlib/Topology/Maps.lean | IsOpenMap.of_nhds_le | [] | [
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Mathlib/Analysis/Convex/Quasiconvex.lean | QuasilinearOn.dual | [] | [
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Mathlib/Data/List/Sigma.lean | List.dlookup_kunion_left | [
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.CG.of_map_embedding | [
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Mathlib/Algebra/Ring/CompTypeclasses.lean | RingHomSurjective.comp | [
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Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_and_le_inf | [
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.mem_integer_iff | [
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.comap_incl_eq_bot | [
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.locallyIntegrableOn_univ | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_pos_iff_exists_mem | [] | [
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictDerivAt.to_localInverse | [] | [
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Mathlib/Analysis/Normed/Group/Basic.lean | ULift.nnnorm_def | [] | [
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Mathlib/Data/Option/NAry.lean | Option.map₂_map_left_comm | [
{
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Mathlib/Data/Finset/Basic.lean | Finset.not_ssubset_empty | [] | [
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Mathlib/Data/List/Basic.lean | List.foldl_op_eq_op_foldr_assoc | [
{
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Functor.asEquivalence_functor | [] | [
539,
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Mathlib/Data/List/Perm.lean | List.Perm.subperm_right | [] | [
415,
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Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.interedges_biUnion | [] | [
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35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const | [
{
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Mathlib/Order/Cover.lean | covby_of_eq_or_eq | [] | [
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Mathlib/Data/Pi/Algebra.lean | Pi.inv_def | [] | [
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Mathlib/Order/LiminfLimsup.lean | Filter.isBoundedUnder_of | [] | [
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Mathlib/Order/RelClasses.lean | ssubset_iff_subset_ne | [] | [
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_multiset_prod | [] | [
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Mathlib/Data/List/MinMax.lean | List.le_maximum_of_mem | [] | [
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Mathlib/Data/PNat/Basic.lean | PNat.add_one_le_iff | [] | [
173,
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Mathlib/Data/Real/EReal.lean | EReal.neg_eq_top_iff | [] | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_re | [] | [
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.aestronglyMeasurable | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_apply | [] | [
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Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_comp | [
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.coe_add | [] | [
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.symm_continuousLinearEquivAt_eq | [] | [
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.mem_neg | [] | [
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Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_add_le_iff_left | [
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Mathlib/Topology/Algebra/Order/Floor.lean | continuousOn_floor | [] | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_map | [
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Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean | CategoryTheory.Idempotents.karoubiUniversal₂_functor_eq | [] | [
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_iInf | [] | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_inj | [] | [
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.Polynomial.quotQuotEquivComm_mk | [
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_add_measure | [] | [
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Mathlib/Data/Fintype/Pi.lean | Fintype.piFinset_univ | [] | [
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.toAddSubsemigroup'_closure | [] | [
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Mathlib/RingTheory/Localization/Integral.lean | IsLocalization.integerNormalization_coeff | [
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Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.symm_mulRight₀ | [] | [
215,
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213,
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Mathlib/Analysis/SpecialFunctions/Sqrt.lean | Real.deriv_sqrt_aux | [
{
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60,
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Mathlib/Data/Sigma/Basic.lean | Sigma.subtype_ext | [] | [
82,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.charpoly_degree_eq_dim | [
{
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_inf | [] | [
228,
6
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227,
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Mathlib/Topology/UniformSpace/Separation.lean | Filter.HasBasis.separationRel | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² ... | [
190,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/Algebra/Lie/Abelian.lean | LieModule.trivial_iff_le_maximal_trivial | [] | [
159,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
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Mathlib/Algebra/Group/Basic.lean | leftInverse_inv | [] | [
279,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
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Mathlib/Data/Prod/Basic.lean | Prod.fst_injective | [] | [
150,
44
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149,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | Filter.EventuallyEq.restrict | [
{
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Mathlib/RepresentationTheory/Action.lean | Action.leftUnitor_hom_hom | [
{
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529,
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527,
1
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | one_lt_of_lt_mul_right | [
{
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}
] | [
477,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.norm_mul_mem_unitary | [] | [
262,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_prod | [
{
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1454,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_sub_int_mul_pi | [] | [
1047,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_le | [] | [
170,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.isBigO_congr_left | [] | [
183,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_z | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.count_normalizedFactors_eq | [] | [
1233,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.equivOfMinpoly_symm | [] | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.subgroup_mul_singleton | [
{
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"tact... | [
378,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.Bounded.cthickening | [
{
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"state_before": "ι : ... | [
1132,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
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Std/Data/List/Init/Lemmas.lean | List.foldlM_reverse | [] | [
160,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
159,
9
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_C | [] | [
353,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.det_eq_sum_mul_adjugate_row | [
{
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"state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝... | [
443,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformly.comp | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng✝ : ι → α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace γ\nh : TendstoLocallyUniformlyOn F f p univ\ng : γ → α\ncg : Continuous g\n⊢ Te... | [
728,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.comp_eq_id | [] | [
328,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.lift_rank_comp_le | [] | [
1348,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.biUnion_smul_finset | [] | [
1681,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.b_eq_three_roots | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1023752\nS : Type ?u.1023755\nF : Type u_1\nK : Type u_2\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : roots (map φ P) = {x, y, z}\n⊢ ↑φ P.b = ↑φ P.a * -(x + y + z)",
"tactic": "injection eq_sum_three... | [
544,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.bot_eq_one | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ext_inner_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1813291\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\nh : ∀ (v : E), inner x v = inner y... | [
697,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_zero | [] | [
163,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_one_div_le_one | [
{
"state_after": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nM N : Submodule R A\nm n : A\nI : Submodule R A\n⊢ ∀ (m : A), m ∈ I → ∀ (n : A), n ∈ 1 / I → m * n ∈ 1",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v... | [
725,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Pi.coe_nat | [] | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_zero_of_eq_zero | [] | [
226,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.map_id_id | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ inl ≫ map (𝟙 X) (𝟙 Y) = inl ≫ 𝟙 (X ⨿ Y)\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ inr ≫ map (𝟙 X) (𝟙 Y) = inr ≫ 𝟙 (X ⨿ Y)",
"state_before": "... | [
855,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.lt_trans | [
{
"state_after": "case h.e'_3\nα : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f < g\ngh : g < h\n⊢ h - f = g - f + (h - g)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f < g\ngh : g < h\n⊢ Pos (h - f)",
"tactic": "convert add_pos fg gh... | [
741,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean | Real.sin_lt | [
{
"state_after": "case inl\nx : ℝ\nh : 0 < x\nh' : 1 < x\n⊢ sin x < x\n\ncase inr\nx : ℝ\nh : 0 < x\nh' : x ≤ 1\n⊢ sin x < x",
"state_before": "x : ℝ\nh : 0 < x\n⊢ sin x < x",
"tactic": "cases' lt_or_le 1 x with h' h'"
},
{
"state_after": "case inr\nx : ℝ\nh : 0 < x\nh' : x ≤ 1\nhx : abs x = x\n... | [
58,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.not_tendsto_const_atBot | [] | [
115,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.sub_byteIdx | [] | [
101,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
101,
9
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_sup | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.113297\n𝕜 : Type ?u.113300\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑(edgeSet G)\ninst✝² : Fintype ↑(edgeSet G₁)\ninst✝¹ : Fintype ↑(edgeSet G₂)\... | [
928,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.kernel_eq_kernel | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\ni j j' : ι\nr : ComplexShape.Rel c i j\nr' : ComplexShape.Rel c i j'\n⊢ kernelSubobject (d C i j' ≫ eqToHom (_ : X C j' = X C j)) = kernelSubobject ... | [
338,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iUnion_Iic_coe_nat | [] | [
869,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.measurableSet_lt | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.225359\nι : Type ?u.225362\ninst✝⁴ : Countable ι\nf✝ g✝ : α → β\nm : MeasurableSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : LinearOrder β\ninst✝¹ : OrderClosedTopology β\ninst✝ : PseudoMetrizableSpace β\nf g : α → β\nhf : StronglyMeasurable f\nhg : Str... | [
877,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.add_right | [] | [
118,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.uniformContinuous_inv | [] | [
102,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/LinearAlgebra/Charpoly/Basic.lean | LinearMap.aeval_eq_aeval_mod_charpoly | [] | [
90,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquiv_trans | [] | [
1107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
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