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/SpecificLimits/Normed.lean | NormedField.continuousAt_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.67516\nβ : Type ?u.67519\nι : Type ?u.67522\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\n⊢ ContinuousAt Inv.inv x ↔ x ≠ 0",
"tactic": "simpa [(zero_lt_one' ℤ).not_le] using @continuousAt_zpow _ _ (-1) x"
}
] | [
90,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_disjUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nh : Disjoint (Prepartition.iUnion π₁) (Prepartition.iUnion π₂)\n⊢ Prepartition.iUnion (disjUnion π₁ π₂ h) = Prepartition.iUnion π₁ ∪ Prepartition.iUn... | [
658,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inv_aux | [] | [
620,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Icc ↑a ↑b = Icc a b",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
168,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.map_refl | [
{
"state_after": "case h.h.a.h\nα : Type u_1\nβ : Type ?u.106343\nγ : Type ?u.106346\nι : Sort ?u.106349\nκ : ι → Sort ?u.106354\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α ≃o β\ns t : LowerSet α\na : α\nb : β\nx✝¹ : LowerSet α\nx✝ : α\n⊢ x✝ ∈ ↑(↑(map (OrderIso.refl α)) x✝¹) ↔ x✝ ∈ ↑(↑(... | [
1028,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.indep_generateFrom_le_nat | [] | [
501,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
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Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_max | [] | [
116,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.obj_μ_inv_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)\nm₁ m₂ m₃ : M\nX : C\n⊢ inv ((F.obj m₃).map ((MonoidalFunctor.μIso F m₁ m₂).inv.app X)) =\n inv\n ((LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor (m₁ ⊗ m₂) m₃).ap... | [
280,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/Order/CompleteLattice.lean | sInf_image2 | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nβ₂ : Type ?u.175983\nγ : Type u_2\nι : Sort ?u.175989\nι' : Sort ?u.175992\nκ : ι → Sort ?u.175997\nκ' : ι' → Sort ?u.176002\ninst✝ : CompleteLattice α\nf✝ g s✝ t✝ : ι → α\na b : α\nf : β → γ → α\ns : Set β\nt : Set γ\n⊢ sInf (image2 ... | [
1617,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.map_nullHomotopicMap' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.267671\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni✝ : ι\nW : Type ?u.268026\ninst✝² : Category W\ninst✝¹ : Preadditive W\nG : V ⥤ W\ninst✝ : Functor.Additiv... | [
334,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Dynamics/PeriodicPts.lean | Function.isPeriodicPt_zero | [] | [
73,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Mathlib/Init/Logic.lean | of_heq_true | [] | [
78,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.660548\nm : MeasurableSpace α\nμ ν : Measure α\nc : ComplexMeasure α\ninst✝ : HaveLebesgueDecomposition c μ\n⊢ singularPart c μ + Measure.withDensityᵥ μ (rnDeriv c μ) = SignedMeasure.toComplexMeasure (↑re c) (↑im c)",
"state_before": "α : Type u_1\nβ : Type ?u.660... | [
1243,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
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Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.nonempty | [
{
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93,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.exists_le_hasSum_of_le | [
{
"state_after": "α : Type ?u.310040\nβ : Type u_1\nγ : Type ?u.310046\nf g : β → ℝ≥0\nr : ℝ≥0\nhgf : ∀ (b : β), g b ≤ f b\nhfr : HasSum f r\nb : β\n⊢ ↑(g b) ≤ ↑(f b)",
"state_before": "α : Type ?u.310040\nβ : Type u_1\nγ : Type ?u.310046\nf g : β → ℝ≥0\nr : ℝ≥0\nhgf : ∀ (b : β), g b ≤ f b\nhfr : HasSum f r... | [
1113,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.union_smul | [] | [
196,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | Commute.zpow_self₀ | [] | [
136,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.unbounded_range_of_sup_ge | [] | [
1356,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1350,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparating_iff_epi | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\n𝒢 : Set C\ninst✝ : ∀ (A : C), HasCoproduct fun f => ↑f.fst\nh : IsSeparating 𝒢\nA Z✝ : C\nu v : A ⟶ Z✝\nhuv : Sigma.desc Sigma.snd ≫ u = Sigma.desc Sigma.snd ≫ v\nG : C\nhG : G ∈ 𝒢\nf : G ⟶ A\n⊢ f ≫ u = f ≫ ... | [
267,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
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Mathlib/Algebra/GroupPower/Basic.lean | dvd_pow | [
{
"state_after": "α : Type ?u.46449\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\nx y : M\nhxy : x ∣ y\nn : ℕ\nx✝ : n + 1 ≠ 0\n⊢ x ∣ y * y ^ n",
"state_before": "α : Type ?u.46449\nM : Type u\nN : Type v\nG : Type w... | [
238,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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] |
Mathlib/Data/W/Constructions.lean | WType.leftInverse_nat | [
{
"state_after": "f : Natβ Natα.zero → WType Natβ\n⊢ mk Natα.zero Empty.elim = mk Natα.zero f",
"state_before": "f : Natβ Natα.zero → WType Natβ\n⊢ ofNat (toNat (mk Natα.zero f)) = mk Natα.zero f",
"tactic": "rw [toNat, ofNat]"
},
{
"state_after": "case e_f\nf : Natβ Natα.zero → WType Natβ\n⊢ Em... | [
77,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.seq_mono | [] | [
2641,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2639,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_empty | [] | [
649,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
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] |
Mathlib/Data/Set/Sups.lean | upperClosure_sups | [
{
"state_after": "case a.h\nα : Type u_1\ninst✝ : SemilatticeSup α\ns t : Set α\na : α\n⊢ a ∈ ↑(upperClosure (s ⊻ t)) ↔ a ∈ ↑(upperClosure s ⊔ upperClosure t)",
"state_before": "α : Type u_1\ninst✝ : SemilatticeSup α\ns t : Set α\n⊢ upperClosure (s ⊻ t) = upperClosure s ⊔ upperClosure t",
"tactic": "ext... | [
409,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_toSubmonoid | [] | [
436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
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Mathlib/Data/List/Infix.lean | List.prefix_iff_eq_append | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.3114\nl l₁ l₃ : List α\na b : α\nm n : ℕ\nr : List α\n⊢ l₁ ++ drop (length l₁) (l₁ ++ r) = l₁ ++ r",
"state_before": "α : Type u_1\nβ : Type ?u.3114\nl l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\n⊢ l₁ <+: l₂ → l₁ ++ drop (length l₁) l₂ = l₂",
"tactic": "r... | [
203,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafifyMap_comp | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q R : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nγ : Q ⟶ R\n⊢ plusMap J (plusMa... | [
493,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
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] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.basis_repr_symm_apply' | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\ninst✝⁴ : CommRing k\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : Algebra k R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module k M\nι : Type u_4\nb : Basis ι k M\nr : R\ni : ι\n⊢ r • ↑(basis R b) i = r ⊗ₜ[k] ↑b i",
"tactic": "simpa using basi... | [
1071,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.range_pullback_to_prod | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z✝ : TopCat\nX Y Z : TopCat\nf : X ⟶ Z\ng : Y ⟶ Z\nx : (forget TopCat).obj (X ⨯ Y)\n⊢ x ∈ Set.range ((forget TopCat).map (prod.lift pullback.fst pullback.snd)) ↔\n x ∈ {x | (forget TopCat).map (prod.fst ≫ f) x = (forget TopCat).map (prod.sn... | [
175,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.76691\nα : Type u_1\nβ : Type ?u.76697\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhb : 0 < b\n⊢ a / b < 1 ↔ a < b",
"tactic": "rw [div_lt_iff hb, one_mul]"
}
] | [
433,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.mul_fst | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measurable_superset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14385\nγ : Type ?u.14388\nδ : Type ?u.14391\nι : Type ?u.14394\ninst✝ : MeasurableSpace α\nμ✝ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\nμ : Measure α\ns : Set α\n⊢ ∃ t, s ⊆ t ∧ MeasurableSet t ∧ ↑↑μ t = ↑↑μ s",
"tactic": "simpa only [←... | [
210,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.map_le_iff_le_comap | [] | [
736,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
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] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.continuousOn_log | [
{
"state_after": "x y : ℝ\n⊢ Continuous fun x => log ↑x",
"state_before": "x y : ℝ\n⊢ ContinuousOn log ({0}ᶜ)",
"tactic": "simp only [continuousOn_iff_continuous_restrict, restrict]"
},
{
"state_after": "x y : ℝ\n⊢ Continuous fun x => ↑(OrderIso.symm expOrderIso) { val := abs ↑x, property := (_ ... | [
307,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.stronglyMeasurable | [] | [
137,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
11
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LieRing.of_associative_ring_bracket | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/Bases.lean | RingFilterBasis.submodulesBasisIsBasis | [
{
"state_after": "ι : Type u_3\nR : Type u_1\nA : Type ?u.51903\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nBR : RingFilterBasis R\nB : ι → Submodule R M\nhB : SubmodulesBasis BR B\nx✝ : TopologicalSpace R := topology BR\nthis : Top... | [
405,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
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] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.pow_mod_card_support_cycleOf_self_apply | [
{
"state_after": "case pos\nι : Type ?u.2520927\nα : Type u_1\nβ : Type ?u.2520933\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y : α\nf : Perm α\nn : ℕ\nx : α\nhx : ↑f x = x\n⊢ ↑(f ^ (n % card (support (cycleOf f x)))) x = ↑(f ^ n) x\n\ncase neg\nι : Type ?u.2520927\nα : Type u_1\nβ : Type ?u.... | [
1173,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.intDegree_add | [] | [
1628,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1623,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.repeat_add | [
{
"state_after": "m n : ℕ\nα✝ : Fin (n + 1) → Type u\nx : α✝ 0\nq : (i : Fin (n + 1)) → α✝ i\np : (i : Fin n) → α✝ (succ i)\ni : Fin n\ny : α✝ (succ i)\nz : α✝ 0\nα : Type u_1\na : Fin n → α\nm₁ m₂ : ℕ\nh : (m₁ + m₂) * n = m₁ * n + m₂ * n\n⊢ repeat (m₁ + m₂) a = append (repeat m₁ a) (repeat m₂ a) ∘ ↑(cast h)",
... | [
415,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_inv | [] | [
791,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Algebra/Field/Basic.lean | neg_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.34433\nβ : Type ?u.34436\nK : Type u_1\ninst✝¹ : DivisionMonoid K\ninst✝ : HasDistribNeg K\na b : K\n⊢ -a⁻¹ = (-a)⁻¹",
"tactic": "rw [inv_eq_one_div, inv_eq_one_div, div_neg_eq_neg_div]"
}
] | [
127,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_inv | [
{
"state_after": "case pos\nx✝ y x : ℝ\nhx : x = 0\n⊢ log x⁻¹ = -log x\n\ncase neg\nx✝ y x : ℝ\nhx : ¬x = 0\n⊢ log x⁻¹ = -log x",
"state_before": "x✝ y x : ℝ\n⊢ log x⁻¹ = -log x",
"tactic": "by_cases hx : x = 0"
},
{
"state_after": "no goals",
"state_before": "case neg\nx✝ y x : ℝ\nhx : ¬x =... | [
142,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_Ioc | [] | [
716,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_sum_elim | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type u_1\nδ : Type ?u.143893\nε : Type ?u.143896\nζ : Type ?u.143899\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → γ\ng : β → γ\n⊢ IsOpenMap (Sum.elim f g) ... | [
980,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
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Mathlib/Data/Set/Lattice.lean | Set.monotone_preimage | [] | [
1711,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1711,
1
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.surjective_stableUnderComposition | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type ?u.89599\ninst✝¹ : Category D\ninst✝ : ConcreteCategory C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhf : MorphismProperty.surjective C f\nhg : MorphismProperty.surjective C g\n⊢ Surjective ((forget C).map (f ≫ g))",
"state_before": "C : Type u\ninst✝² : Ca... | [
650,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
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Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eq | [
{
"state_after": "case intro.intro.intro.intro.intro\nι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr✝ r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ✝ π₁ π₂ : TaggedPrepartition I\nl✝ l₁ l₂ l : IntegrationParams\nπ₀ : Prepartition I\nhc₁ : Prepartition.distortion π₀ ≤ c\nhc₂ : Prepartition.distortion (Prepart... | [
528,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.equivCongr_apply_apply | [] | [
421,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
9
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Mathlib/SetTheory/Lists.lean | Lists'.Subset.trans | [] | [
454,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.smul_sup | [] | [
391,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/Algebra/Regular/Basic.lean | isRegular_iff_subsingleton | [] | [
234,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Order/Circular.lean | sbtw_cyclic | [] | [
234,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_apply | [
{
"state_after": "no goals",
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"tactic": "rw [cond, Measure.smul_apply, Measure.restrict_apply' hms, Set.inter_comm, smul_eq_mul]"
... | [
106,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Analysis/Normed/Order/Lattice.lean | norm_le_norm_of_abs_le_abs | [] | [
58,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.stalkMap.id | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX : PresheafedSpace C\nx : ↑↑X\n⊢ (stalkFunctor C ((CategoryTheory.forget TopCat).map (𝟙 ↑X) x)).map (𝟙 X).c ≫ stalkPushforward C (𝟙 ↑X) X.presheaf x =\n 𝟙 (stalk X x)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ :... | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Analysis/Complex/Basic.lean | IsROrC.hasSum_re | [] | [
527,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isOrtho_zero_left | [] | [
765,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.prod_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.390033\nM₆ : Type ?u.390036\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R... | [
733,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_empty | [] | [
623,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.abs_exp_sub_one_sub_id_le | [
{
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"state_before": "x : ℂ\nhx : ↑abs x ≤ 1\n⊢ ↑abs (exp x - 1 - x) = ↑abs (exp x - ∑ m in range 2, x ^ m / ↑(Nat.factorial m))",
"tactic": "simp [sub_eq_add_neg, sum_range_succ_comm, add_assoc]"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : ↑abs x ≤ 1... | [
1694,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.aeSeq_eq_fun_ae | [] | [
125,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Analysis/Calculus/FDeriv/Star.lean | differentiableWithinAt_star_iff | [] | [
67,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Preconnected.set_univ_walk_nonempty | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nhconn : Preconnected G\nu v : V\n⊢ Nonempty (Walk G u v)",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nhconn : Pr... | [
2204,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2201,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.inv | [] | [
199,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ext | [] | [
139,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_pow | [] | [
1534,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
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src/lean/Init/SimpLemmas.lean | and_true | [] | [
83,
88
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
83,
9
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.prev | [
{
"state_after": "case refl\nc : Char\nl r : List Char\nh :\n ValidFor (c :: l) r\n { s := { data := List.reverse (c :: l) ++ r }, i := { byteIdx := utf8Len (List.reverse (c :: l)) } }\n⊢ ValidFor l (c :: r)\n (Iterator.prev { s := { data := List.reverse (c :: l) ++ r }, i := { byteIdx := utf8Len (List.r... | [
559,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
554,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.not_terminates_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ ¬Terminates s ↔ ∀ (n : ℕ), Option.isSome (get? s n) = true",
"tactic": "simp only [Terminates, TerminatedAt, ← Ne.def, Option.ne_none_iff_isSome, not_exists, iff_self]"
}
] | [
136,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_induction₂ | [] | [
696,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
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Mathlib/Algebra/BigOperators/Order.lean | Finset.one_lt_prod' | [] | [
521,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
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Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorph.continuous | [] | [
123,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
11
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.nhds_eq_comap | [] | [
384,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.subseq_mem | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nV : ℕ → Set (α × α)\nhV : ∀ (n : ℕ), V n ∈ 𝓤 α\nu : ℕ → α\nhu : CauchySeq u\nthis : ∀ (n : ℕ), ∃ N, ∀ (k : ℕ), k ≥ N → ∀ (l : ℕ), l ≥ k → (u l, u k) ∈ V n\n⊢ ∃ φ, StrictMono φ ∧ ∀ (n : ℕ), (u (φ (n + 1)), u (φ n)) ∈ V n",
"state_before": "α ... | [
266,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/Algebra/Ring/Ideal.lean | QuotientRing.quotientMap_coe_coe | [
{
"state_after": "case mk.mk.mk\nR : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : CommRing R\nN : Ideal R\ninst✝ : TopologicalRing R\nfst✝ snd✝ : R ⧸ N\nx y : R\n⊢ ∃ a, (fun p => (↑(mk N) p.fst, ↑(mk N) p.snd)) a = (Quot.mk Setoid.r x, Quot.mk Setoid.r y)",
"state_before": "R : Type u_1\ninst✝² : Topolog... | [
71,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleMap_zero | [] | [
115,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_one | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : CommRing K\n⊢ { toFractionRing := 1 } = 1",
"tactic": "simp only [One.one, OfNat.ofNat, RatFunc.one]"
}
] | [
370,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.tail_update_succ | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\ni : Fin n\ny : α (succ i)\nz : α 0\nj : Fin n\n⊢ tail (update q (succ i) y) j = update (tail q) i y j",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nx : α 0\nq : (i : Fin (... | [
233,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/List/Func.lean | List.Func.length_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : Neg α\nas : List α\n⊢ length (neg as) = length as",
"tactic": "simp only [neg, length_map]"
}
] | [
271,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_eq_range | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.92494\nι : Sort ?u.92497\nι' : Sort ?u.92500\nf✝ : ι → α\ns✝ t : Set α\nf : α → β\ns : Set α\nx✝ : β\n⊢ x✝ ∈ f '' s ↔ x✝ ∈ range fun x => f ↑x",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.92494\nι : Sort ?u.92497\nι' : Sort ?u.9... | [
1071,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.succ_add | [] | [
120,
43
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
118,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | extremePoints_prod | [
{
"state_after": "case h\n𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nι : Type ?u.13373\nπ : ι → Type ?u.13378\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : AddCommGroup F\ninst✝³ : (i : ι) → AddCommGroup (π i)\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 F\ninst✝ : (i : ι) → Module 𝕜 (π i)\nA B ... | [
215,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_update_smul | [
{
"state_after": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁸ : CommSemiring R\ninst✝⁷ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁶ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁵ : AddCommMonoid M₂\ninst✝⁴ : (i : Fin (Nat.... | [
868,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_bit0_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : DivisionMonoid α\ninst✝ : HasDistribNeg α\nx : α\nn : ℤ\n⊢ (-x) ^ bit0 n = x ^ bit0 n",
"tactic": "rw [zpow_bit0', zpow_bit0', neg_mul_ne... | [
185,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_lift | [] | [
239,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_le | [] | [
488,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.singleton_disjoint_neighborFinset | [] | [
1366,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.compactSpace_iff_bounded_univ | [] | [
2534,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2533,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_congr | [
{
"state_after": "F : Type ?u.17780\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.17789\nι : Type ?u.17792\nκ : Type ?u.17795\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns s₁ : Finset β\nf✝ g✝ : β → α\na : α\nf g : β → α\nhfg : ∀ (a : β), a ∈ s₁ → f a = g a\n⊢ sup s₁ f = sup s₁ g",
"state_before": "F : Type ... | [
95,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Order/Max.lean | IsTop.isMax | [] | [
228,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Data/Int/Interval.lean | Int.card_fintype_Icc_of_le | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nh : a ≤ b + 1\n⊢ ↑(Fintype.card ↑(Set.Icc a b)) = b + 1 - a",
"tactic": "rw [card_fintype_Icc, toNat_sub_of_le h]"
}
] | [
167,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.coe_linear_eq_coe_contLinear | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_nonneg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.15095\nι : Type ?u.15098\nκ : Type ?u.15101\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ns : Finset α\nt : Finse... | [
136,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.contLinear_map_vsub | [] | [
102,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_map_left | [
{
"state_after": "case h.e'_2.h.e'_6\nα : Type u\nβ : Type u_2\nγ : Type u_3\nδ : Type u_1\nε : Type ?u.35705\nf : α → β → γ\ng : δ → α\nl : List δ\nl' : List β\n⊢ l' = map id l'",
"state_before": "α : Type u\nβ : Type u_2\nγ : Type u_3\nδ : Type u_1\nε : Type ?u.35705\nf : α → β → γ\ng : δ → α\nl : List δ\... | [
149,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonneg_add_lem | [
{
"state_after": "d x y z w : ℕ\nxy : Nonneg { re := ↑x, im := -↑y }\nzw : Nonneg { re := -↑z, im := ↑w }\nthis : Nonneg { re := subNatNat x z, im := subNatNat w y }\n⊢ Nonneg ({ re := ↑x, im := -↑y } + { re := -↑z, im := ↑w })",
"state_before": "d x y z w : ℕ\nxy : Nonneg { re := ↑x, im := -↑y }\nzw : Nonn... | [
691,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_mul_lt_sum_mul_comp_perm_iff | [] | [
519,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.conjTranspose_nonsing_inv | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.187052\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA B : Matrix n n α\ninst✝ : StarRing α\n⊢ A⁻¹ᴴ = Aᴴ⁻¹",
"tactic": "rw [inv_def, inv_def, conjTranspose_smul, det_conjTranspose, adjugate... | [
298,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Std/Logic.lean | iff_def | [] | [
38,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
38,
1
] |
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