file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.differentiableAt | [] | [
278,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_sup | [] | [
1666,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1665,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.starHom_apply | [] | [
100,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.coe_injective | [
{
"state_after": "case mk\nα : Type u_2\nβ : Type ?u.7089\nm : MeasurableSpace α\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nw : VectorMeasure α M\nmeasureOf'✝ : Set α → M\nempty'✝ : measureOf'✝ ∅ = 0\nnot_measurable'✝ : ∀ ⦃i : Set α⦄, ¬MeasurableSet i → measureOf'✝ i = 0\nm_iUnion'✝ :\... | [
123,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Std/Data/Int/Lemmas.lean | Int.natAbs_ofNat | [] | [
138,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
138,
9
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Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.essentiallySmall_congr | [
{
"state_after": "case mp\nC✝ : Type u\ninst✝² : Category C✝\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\ne : C ≌ D\n⊢ EssentiallySmall C → EssentiallySmall D\n\ncase mpr\nC✝ : Type u\ninst✝² : Category C✝\nC : Type u\ninst✝¹ : Category C\nD : Type u'\ninst✝ : Category D\ne : C ≌ D\n⊢ Esse... | [
78,
43
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_target'' | [] | [
735,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.some_single_none | [
{
"state_after": "case h\nα : Type u_2\nβ : Type ?u.324241\nγ : Type ?u.324244\nι : Type ?u.324247\nM : Type u_1\nM' : Type ?u.324253\nN : Type ?u.324256\nP : Type ?u.324259\nG : Type ?u.324262\nH : Type ?u.324265\nR : Type ?u.324268\nS : Type ?u.324271\ninst✝ : Zero M\nm : M\na✝ : α\n⊢ ↑(some (single none m)) ... | [
831,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_univ_eq_zero | [] | [
1097,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.coe_injective | [] | [
282,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.iff_exists | [
{
"state_after": "ι : Type u_1\nσ : Type u_2\nR : Type ?u.110347\nA : Type u_3\ninst✝⁵ : Semiring A\ninst✝⁴ : SetLike σ A\ninst✝³ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : GradedRing 𝒜\nI : Ideal A\n⊢ I = HomogeneousIdeal.toIdeal (homogeneousCore 𝒜 I) ↔ ∃ S, I ... | [
231,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂_mul_basis_toMatrix | [
{
"state_after": "R : Type u_2\nR₁ : Type ?u.1708981\nR₂ : Type ?u.1708984\nM : Type ?u.1708987\nM₁ : Type u_3\nM₂ : Type u_5\nM₁' : Type ?u.1708996\nM₂' : Type ?u.1708999\nn : Type u_7\nm : Type u_6\nn' : Type u_1\nm' : Type u_4\nι : Type ?u.1709014\ninst✝¹⁶ : CommRing R\ninst✝¹⁵ : AddCommMonoid M₁\ninst✝¹⁴ : ... | [
486,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.homOfLe_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\nh : N ≤ N'\nx ... | [
595,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.embDomain_apply | [] | [
1728,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasColimitOfIso | [
{
"state_after": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F G : J ⥤ C\ninst✝ : HasColimit F\nα : G ≅ F\ns : Cocone G\nj : J\n⊢ (α.hom.app j ≫ colimit.ι F j) ≫ (fun s => colimit.desc F ((Cocones.precompose α.inv).obj s)) s = s.ι.app j",
"state_b... | [
893,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
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Mathlib/Analysis/Convex/Join.lean | convexJoin_singletons | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.34631\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns t s₁ s₂ t₁ t₂ u : Set E\nx✝ y x : E\n⊢ convexJoin 𝕜 {x} {y} = segment 𝕜 x y",
"tactic": "simp"
}
] | [
80,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_cos | [] | [
103,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_pos | [
{
"state_after": "a b : Ordinal\na0 : 0 < a\nh0 : 0 < a ^ 0\n⊢ 0 < a ^ b",
"state_before": "a b : Ordinal\na0 : 0 < a\n⊢ 0 < a ^ b",
"tactic": "have h0 : 0 < (a^0) := by simp only [opow_zero, zero_lt_one]"
},
{
"state_after": "case H₁\na b : Ordinal\na0 : 0 < a\nh0 : 0 < a ^ 0\n⊢ 0 < a ^ 0\n\nca... | [
102,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Std/Data/Int/Lemmas.lean | Int.nonneg_or_nonneg_neg | [] | [
551,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
549,
1
] |
Mathlib/Analysis/PSeries.lean | sum_Ioo_inv_sq_le | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : LinearOrderedField α\nk n : ℕ\n⊢ Ioo k n ⊆ Ioc k (max (k + 1) n)\n\ncase hf\nα : Type u_1\ninst✝ : LinearOrderedField α\nk n : ℕ\n⊢ ∀ (i : ℕ), i ∈ Ioc k (max (k + 1) n) → ¬i ∈ Ioo k n → 0 ≤ (↑(i ^ 2))⁻¹",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedFie... | [
339,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_monomial | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na✝ b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nn : ℕ\na : R\n⊢ eval₂ (RingHom.comp C f) X (↑(monomial n) a) = ↑(monomial n) (↑f a)",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na✝ ... | [
709,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_comp_mono | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Mono g\nh✝ : f ≫ g = 0\nh : f = 0\n⊢ f = 0",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroMorphism... | [
142,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.addSubmonoid_closure_setOf_eq_monomial | [
{
"state_after": "case h\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ ⊤ ≤ AddSubmonoid.closure {p | ∃ n a, p = ↑(monomial n) a}",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ AddSubmonoid.closure {p | ∃ n a, p = ↑(monomial n) a} = ⊤",
"tactic": "ap... | [
806,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.eq_iff_veq | [] | [
195,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.ofNatCast | [] | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_le_two_norm | [] | [
222,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.IsBounded.pi | [] | [
113,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Subalgebra.finiteDimensional_toSubmodule | [] | [
1367,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.map_mk | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.mem_ofSet_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α\ninst✝¹ : DecidablePred fun x => x ∈ s✝\ns : Set α\ninst✝ : DecidablePred fun x => x ∈ s\na b : α\n⊢ (a ∈ if b ∈ s then some b else none) ↔ a = b ∧ a ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ns✝ : Set α... | [
233,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.lift_of | [] | [
127,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_zero | [] | [
186,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderivWithin_const_mul | [] | [
499,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.pow_sub' | [
{
"state_after": "case h\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nm n : ℕ\nha : IsUnit (det A)\nh : n ≤ m\n⊢ IsUnit (det (A ^ n))",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA ... | [
55,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.sub_strictConvexOn | [] | [
912,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_toMatrix | [
{
"state_after": "R : Type ?u.421389\ninst✝⁹ : CommRing R\nM : Type u_3\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nM' : Type ?u.421980\ninst✝⁶ : AddCommGroup M'\ninst✝⁵ : Module R M'\nι : Type u_1\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ne : Basis ι R M\nA : Type u_2\ninst✝² : CommRing A\ninst✝¹ : Modul... | [
216,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.right_unitality_app | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nn : M\nX : C\nthis :\n (ρ_ (F.obj n)).hom.app X =\n ((𝟙 (F.obj n) ⊗ F.ε) ≫ LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor n (𝟙_ M) ≫ F.map (ρ_ n).hom).app X\n⊢ F.ε.... | [
218,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_piecewise_of_subset_right | [] | [
2523,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2520,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_pos | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sqrt x ≤ 0 ↔ sqrt x = 0",
"tactic": "simp [le_antisymm_iff, sqrt_nonneg]"
}
] | [
352,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/LinearAlgebra/Vandermonde.lean | Matrix.eq_zero_of_forall_index_sum_pow_mul_eq_zero | [] | [
163,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_inv | [] | [
631,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.eq_ftaylor_series_of_uniqueDiffOn | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ ... | [
998,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Order/Bounds/Basic.lean | Set.subsingleton_of_isLUB_le_isGLB | [] | [
1098,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | min_le_mul_of_one_le_right | [] | [
138,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_of_fun_eq_integral | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.949136\n𝕜 : Type ?u.949139\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
928,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.CG.map_of_surjective | [
{
"state_after": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : CG L M\nf : M →[L] N\nhs : Hom.range f = ⊤\n⊢ CG L N",
"state_before": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : CG L M\nf : M →[L] N\nhs : Funct... | [
247,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/NumberTheory/Liouville/Residual.lean | setOf_liouville_eq_iInter_iUnion | [
{
"state_after": "case h\nx : ℝ\n⊢ x ∈ {x | Liouville x} ↔ x ∈ ⋂ (n : ℕ), ⋃ (a : ℤ) (b : ℤ) (_ : 1 < b), ball (↑a / ↑b) (1 / ↑b ^ n) \\ {↑a / ↑b}",
"state_before": "⊢ {x | Liouville x} = ⋂ (n : ℕ), ⋃ (a : ℤ) (b : ℤ) (_ : 1 < b), ball (↑a / ↑b) (1 / ↑b ^ n) \\ {↑a / ↑b}",
"tactic": "ext x"
},
{
"... | [
33,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_add_left | [
{
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333,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isBoundedUnder_ge_exp_comp | [] | [
207,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Data/Int/Cast/Basic.lean | Int.cast_two | [
{
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"tactic": "rw [cast_ofNat, Nat.cast_ofNat]"
}
] | [
155,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Data/Subtype.lean | Subtype.val_inj | [] | [
134,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.im_neg | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulMono_iff_covariant_pos | [
{
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455,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.comp_apply | [] | [
174,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_fst_prod' | [
{
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940,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.integrable_of_hasCompactSupport | [] | [
308,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Ico' | [] | [
2984,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2983,
1
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Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_add | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.degree_coe_units | [] | [
226,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_submatrix_sum_swap_right | [
{
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176,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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Mathlib/Order/Bounds/Basic.lean | isGreatest_Icc | [] | [
688,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_zero_of_not_dvd | [
{
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"tactic": "simp [factorization_eq_zero_iff, h]"
}
] | [
169,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Algebra/Order/WithZero.lean | div_le_div_right₀ | [
{
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}
] | [
241,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivAt.complexToReal_fderiv | [
{
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"tactic": "simpa only [Complex.restrictScalars_one_smulRight] using h.hasFDerivAt.r... | [
128,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Data/Multiset/Interval.lean | Multiset.card_Icc | [
{
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"tactic": "simp_rw [Icc_eq, Finset.card_map, Dfinsupp.card_Icc, Nat.card_Icc, Multise... | [
59,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.arrowCongr_trans | [] | [
2353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2348,
1
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Mathlib/Init/IteSimp.lean | if_true_left_eq_or | [
{
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}
] | [
30,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_smul | [
{
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900,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
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Mathlib/Data/Finset/Prod.lean | Finset.product_eq_empty | [
{
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"tactic": "rw [← not_nonempty_iff_eq_empty, nonempty_product, not_and_or, not_nonempty_iff_eq_empty,\n... | [
213,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Logic.lean | forall_eq' | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ (∀ (a : α), a' = a → p a) ↔ p a'",
"tactic": "simp [@eq_comm _ a']"
}
] | [
450,
92
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
450,
9
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Mathlib/Topology/SubsetProperties.lean | isCompact_empty | [] | [
392,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | indicator_ae_eq_zero_of_restrict_ae_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4867261\nδ : Type ?u.4867264\nι : Type ?u.4867267\nR : Type ?u.4867270\nR' : Type ?u.4867273\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t : Set α\nf : α → β\ninst✝ : Zero β\nhs : MeasurableSet s\nhf : ∀ᵐ (x : α) ∂μ, x ∈ s → f x = OfNat.o... | [
4687,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4681,
1
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Mathlib/Analysis/Convex/Segment.lean | openSegment_translate_preimage | [] | [
280,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_le_fp | [] | [
483,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.interior_preimage | [] | [
282,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/ContinuousOn.lean | self_mem_nhdsWithin | [] | [
153,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Topology/Basic.lean | Filter.HasBasis.lift'_closure | [] | [
584,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_liminf_sum_nat | [] | [
853,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
11
] |
Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.IsTransitive.powerset | [
{
"state_after": "x y✝ z✝ : ZFSet\nh : IsTransitive x\ny : ZFSet\nhy : y ⊆ x\nz : ZFSet\nhz : z ∈ y\n⊢ z ⊆ x",
"state_before": "x y✝ z✝ : ZFSet\nh : IsTransitive x\ny : ZFSet\nhy : y ∈ powerset x\nz : ZFSet\nhz : z ∈ y\n⊢ z ∈ powerset x",
"tactic": "rw [mem_powerset] at hy⊢"
},
{
"state_after": ... | [
93,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Mathlib/Data/Complex/Exponential.lean | Real.abs_exp | [] | [
1503,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Combinatorics/Derangements/Basic.lean | derangements.Equiv.RemoveNone.fiber_none | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.80928\ninst✝ : DecidableEq α\n⊢ fiber none = ∅",
"tactic": "rw [Set.eq_empty_iff_forall_not_mem]"
},
{
"state_after": "α : Type u_1\nβ : Type ?... | [
137,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.singleton | [] | [
230,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
230,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_le_pi | [] | [
104,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.card_support_binomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn m✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nk m : ℕ\nh : k ≠ m\nx y : R\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ card (support (↑C x * X ^ k + ↑C y * X ^ m)) = 2",
"tactic": "rw [support_binomial h hx hy, card_insert_of_not_mem (mt mem_sin... | [
217,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.Integrable.ae_eq_of_forall_set_integral_eq | [
{
"state_after": "α : Type u_2\nE : Type u_1\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\np : ℝ≥0∞\nf g : α → E\nhf : Integrable f\nhg : Integrable g\nhfg : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → (∫ (x : α) in s, f... | [
544,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.sum_pow_mul_eq_add_pow | [] | [
204,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mem_comap | [] | [
200,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | map_iSup₂ | [
{
"state_after": "no goals",
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136,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.div2_zero | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.add_lt_add_iff_left | [
{
"state_after": "no goals",
"state_before": "x y z : PartENat\nhz : z ≠ ⊤\n⊢ z + x < z + y ↔ x < y",
"tactic": "rw [add_comm z, add_comm z, PartENat.add_lt_add_iff_right hz]"
}
] | [
477,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
11
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.isAtom | [] | [
74,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
11
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_deriv_of_nonneg' | [
{
"state_after": "E : Type ?u.158221\nf f' : ℝ → E\ng g' : ℝ → ℝ\na b l : ℝ\nm : E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhderiv : ∀ (x : ℝ), x ∈ Ici a → HasDerivAt g (g' x) x\ng'pos : ∀ (x : ℝ), x ∈ Ioi a → 0 ≤ g' x\nhg : Tendsto g atTop (𝓝 l)\nx : ℝ\nhx : x ∈ Ici a... | [
733,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Order/Bounds/Basic.lean | nonempty_of_not_bddAbove | [] | [
910,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_arrow | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝ : HasKernel f\n⊢ (kernelSubobjectIso f).hom ≫ kernel.ι f = arrow (kernelSubobject f)",
"tactic": "simp [kernelSubobjectIso]"
}
] | [
103,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_union_right | [] | [
342,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_fiberwise | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : Fintype α\ninst✝² : DecidableEq β\ninst✝¹ : Fintype β\ninst✝ : CommMonoid γ\nf : α → β\ng : α → γ\n⊢ ∏ b : β, ∏ a : { a // f a = b }, g ↑a =\n ∏ a : β, ∏ s : { x // f x = a }, g (↑(Equiv.sigmaFiberEquiv f) { fst := a, snd := s })",
"sta... | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_append_comm | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9493\nR S T : α → α → Prop\na : α\nl : List α\ns : Symmetric R\nl₁ l₂ : List α\nthis :\n ∀ (l₁ l₂ : List α), (∀ (x : α), x ∈ l₁ → ∀ (y : α), y ∈ l₂ → R x y) → ∀ (x : α), x ∈ l₂ → ∀ (y : α), y ∈ l₁ → R x y\n⊢ Pairwise R (l₁ ++ l₂) ↔ Pairwise R (l₂ ++ l₁)",
"state_... | [
170,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Involutive.comp_self | [] | [
887,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.measure_limRatioMeas_zero | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.4445000\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
540,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.toFreeSemigroup_comp_map | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nf : α → β\n⊢ ↑(MulHom.comp toFreeSemigroup (map f)) ∘ of = ↑(MulHom.comp (FreeSemigroup.map f) toFreeSemigroup) ∘ of",
"state_before": "α : Type u\nβ : Type v\nf : α → β\n⊢ MulHom.comp toFreeSemigroup (map f) = MulHom.comp (FreeSemigroup.map f) toFreeSemigro... | [
732,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
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