file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | ContinuousOn.locallyIntegrableOn | [] | [
260,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToFun_eq_setToL1 | [
{
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1289,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/FreeModule/Basic.lean | Module.Free.of_equiv' | [] | [
133,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/FieldTheory/PerfectClosure.lean | frobenius_pthRoot | [] | [
67,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.ext_iff_of_sUnion_eq_univ | [
{
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64
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1911,
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Mathlib/Order/Filter/Bases.lean | FilterBasis.generate | [
{
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202,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
11
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Mathlib/Data/List/Rotate.lean | List.mem_cyclicPermutations_self | [
{
"state_after": "case nil\nα : Type u\nl l' : List α\n⊢ [] ∈ cyclicPermutations []\n\ncase cons\nα : Type u\nl✝ l' : List α\nx : α\nl : List α\n⊢ x :: l ∈ cyclicPermutations (x :: l)",
"state_before": "α : Type u\nl✝ l' l : List α\n⊢ l ∈ cyclicPermutations l",
"tactic": "cases' l with x l"
},
{
... | [
616,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
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Mathlib/Logic/Equiv/Fin.lean | finSumFinEquiv_symm_last | [] | [
355,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.congr_left | [] | [
341,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.ext | [] | [
153,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_combine | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np₁ p₂ : Poly\n⊢ denote ctx (combine p₁ p₂) = denote ctx p₁ + denote ctx p₂",
"tactic": "simp [combine, denote_combineAux]"
}
] | [
521,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
520,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.mul_coe_eq_smul | [] | [
1070,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
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] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.smul_nnreal | [] | [
126,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.bot_toAddSubmonoid | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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] |
Mathlib/Data/SetLike/Basic.lean | SetLike.eta | [] | [
181,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndunion_le_union | [] | [
195,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.extend_eq | [] | [
167,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Category/Grpd.lean | CategoryTheory.Grpd.id_to_functor | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | pairwise_disjoint_fiber | [] | [
397,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/CategoryTheory/Adjunction/AdjointFunctorTheorems.lean | CategoryTheory.solutionSetCondition_of_isRightAdjoint | [
{
"state_after": "J : Type v\nC : Type u\ninst✝² : Category C\nD : Type u\ninst✝¹ : Category D\nG : D ⥤ C\ninst✝ : IsRightAdjoint G\nA : C\n⊢ ∃ ι B f, ∀ (X : D) (h : A ⟶ G.obj X), ∃ i g, f i ≫ G.map g = h",
"state_before": "J : Type v\nC : Type u\ninst✝² : Category C\nD : Type u\ninst✝¹ : Category D\nG : D ... | [
80,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns₁ s₂ : Multiset α\n⊢ sup (s₁ + s₂) = fold (fun x x_1 => x ⊔ x_1) (⊥ ⊔ ⊥) (s₁ + s₂)",
"tactic": "simp [sup]"
}
] | [
58,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_pos | [
{
"state_after": "no goals",
"state_before": "o : Ordinal\nho : 0 < o\n⊢ 0 < aleph' o",
"tactic": "rwa [← aleph'_zero, aleph'_lt]"
}
] | [
297,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.tendsto_rightLim_within | [] | [
350,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.symm | [] | [
67,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_of_forall_dual_of_isSeparable | [
{
"state_after": "case intro.intro\nα : Type u_3\nE : Type u_1\n𝕜 : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : IsROrC 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nt : Set E\nf : α → E\nhf : ∀ (c : Dual 𝕜 E), (fun x => ↑c (f x)) =ᵐ[μ] 0\nh't : ∀ᵐ (x : α) ∂μ, f x ∈ t\nd : Set E\nd_... | [
110,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/RingTheory/Prime.lean | Prime.abs | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : CommRing α\ninst✝ : LinearOrder α\np : α\nhp : Prime p\nh : Abs.abs p = p\n⊢ Prime p\n\ncase inr\nα : Type u_1\ninst✝¹ : CommRing α\ninst✝ : LinearOrder α\np : α\nhp : Prime p\nh : Abs.abs p = -p\n⊢ Prime (-p)",
"state_before": "α : Type u_1\ninst✝¹ : CommR... | [
77,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange_id | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : (i : ι) → Zero (β₁ i)\ninst✝ : (i : ι) → Zero (β₂ i)\nh : optParam (∀ (i : ι), id 0 = 0) (_ : ∀ (i : ι), id 0 = id 0)\ng : Π₀ (i : ι), β₁ i\ni✝ : ι\n⊢ ↑(mapRange (fun i =... | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Std/Logic.lean | Or.imp | [] | [
249,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
249,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.prod_eq_of_fintype | [
{
"state_after": "α✝ β α : Type u\nh : Fintype α\n⊢ ∀ (f : α → Cardinal), prod f = lift (∏ i : α, f i)",
"state_before": "α✝ β α : Type u\nh : Fintype α\nf : α → Cardinal\n⊢ prod f = lift (∏ i : α, f i)",
"tactic": "revert f"
},
{
"state_after": "case refine'_1\nα✝ β α : Type u\nh : Fintype α\n⊢... | [
1092,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearEquiv.dualMap_refl | [
{
"state_after": "case h.h\nR : Type u\ninst✝⁴ : CommSemiring R\nM₁ : Type v\nM₂ : Type v'\ninst✝³ : AddCommMonoid M₁\ninst✝² : Module R M₁\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R M₂\nx✝¹ : Dual R M₁\nx✝ : M₁\n⊢ ↑(↑(dualMap (refl R M₁)) x✝¹) x✝ = ↑(↑(refl R (Dual R M₁)) x✝¹) x✝",
"state_before": "R : T... | [
259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.iSup_eq_closure | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.29826\nA : Type ?u.29829\ninst✝¹ : MulOneClass M\ns : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\nι : Sort u_1\np : ι → Submonoid M\n⊢ (⨆ (i : ι), p i) = closure (⋃ (i : ι), ↑(p i))",
"tactic": "simp_rw [Submonoid.clo... | [
558,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Order/Antichain.lean | IsStrongAntichain.insert | [] | [
336,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
11
] |
Mathlib/Data/List/Indexes.lean | List.mapIdxGo_append | [
{
"state_after": "α : Type u\nβ : Type v\nf : ℕ → α → β\nl₁ l₂ : List α\narr : Array β\n⊢ mapIdx.go f (l₁ ++ l₂) arr = mapIdx.go f l₂ (toArray (mapIdx.go f l₁ arr))",
"state_before": "α : Type u\nβ : Type v\n⊢ ∀ (f : ℕ → α → β) (l₁ l₂ : List α) (arr : Array β),\n mapIdx.go f (l₁ ++ l₂) arr = mapIdx.go f ... | [
119,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec2_dotProduct' | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\na₀ a₁ b₀ b₁ : α\n⊢ ![a₀, a₁] ⬝ᵥ ![b₀, b₁] = a₀ * b₀ + a₁ * b₁",
"tactic": "rw [cons_dotProduct_cons, cons_dotProduct_cons, dotProduct_empty, ad... | [
491,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.map_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.346\nf : α → β\np : Pmf α\nb : β\n⊢ ↑(map f p) b = ∑' (a : α), if b = f a then ↑p a else 0",
"tactic": "simp [map]"
}
] | [
53,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/Order/Monoid/TypeTags.lean | Multiplicative.toAdd_le | [] | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.measure_support_lt_top_of_memℒp | [] | [
415,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.irreducible_p | [] | [
615,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.coe_injective | [] | [
90,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Logic/Nontrivial.lean | not_nontrivial | [] | [
123,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_Iic_iff | [] | [
1190,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1189,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.induction_on' | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nP : RatFunc K → Prop\nx : FractionRing K[X]\nf : ∀ (p q : K[X]), q ≠ 0 → P (RatFunc.mk p q)\nx✝ : K[X] × { x // x ∈ K[X]⁰ }\np : K[X]\nq : { x // x ∈ K[X]⁰ }\n⊢ P { toFractionRing := Localization.mk (p, q).fst... | [
292,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
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] |
Mathlib/Order/LocallyFinite.lean | Finset.mem_Icc | [] | [
328,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/FiniteProducts.lean | CategoryTheory.Limits.hasFiniteCoproducts_of_hasCoproducts | [] | [
94,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.has_filtered_colimits_of_has_cofiltered_limits_op | [] | [
329,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_pi | [] | [
1161,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Order/WithBot.lean | WithTop.map_le_iff | [
{
"state_after": "case mono_iff\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.103518\nδ : Type ?u.103521\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\na b : WithTop α\nmono_iff : ∀ {a b : α}, f a ≤ f b ↔ a ≤ b\n⊢ ∀ {a b : αᵒᵈ}, (↑OrderDual.toDual ∘ f ∘ ↑OrderDual.ofDual) a ≤ (↑OrderDual.toDual ∘ f ∘ ↑OrderDua... | [
1161,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_zero | [] | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Std/Data/List/Lemmas.lean | List.eraseP_cons_of_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\np : α → Bool\nh : p a = true\n⊢ eraseP p (a :: l) = l",
"tactic": "simp [eraseP_cons, h]"
}
] | [
932,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
931,
9
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_copy | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prodComparison_inv_natural | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁷ : Category C\nX Y : C\nD : Type u₂\ninst✝⁶ : Category D\nF : C ⥤ D\nA A' B B' : C\ninst✝⁵ : HasBinaryProduct A B\ninst✝⁴ : HasBinaryProduct A' B'\ninst✝³ : HasBinaryProduct (F.obj A) (F.obj B)\ninst✝² : HasBinaryProduct (F.obj A') (F.obj B')\n... | [
1304,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
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Mathlib/Data/Sym/Card.lean | Sym2.card | [] | [
213,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
11
] |
Mathlib/Algebra/Associated.lean | Prime.not_unit | [] | [
40,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.abs_eq | [] | [
918,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.Prepartition.mem_splitCenter | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\n⊢ J ∈ splitCenter I ↔ ∃ s, Box.splitCenterBox I s = J",
"tactic": "simp [splitCenter]"
}
] | [
58,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuous | [] | [
467,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Algebra/Algebra/Pi.lean | AlgEquiv.piCongrRight_trans | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.restrictScalars_mul | [] | [
1549,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.isometry_extend | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.805244\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : PseudoMetricSpace β\ninst✝² : PseudoMetricSpace γ\nf✝ g : α →ᵇ β\nx : α\nC : ℝ\nδ : Type u_1\ninst✝¹ : TopologicalSpace δ\ninst✝ : DiscreteTopology δ\nf : α ↪ δ\nh : δ ... | [
508,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/List/Forall2.lean | List.rel_foldr | [] | [
288,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_eq_preimage_of_inverse | [] | [
409,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.mul_star_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.2929\ninst✝¹ : Semigroup R\ninst✝ : StarSemigroup R\nx : R\n⊢ IsSelfAdjoint (x * star x)",
"tactic": "simpa only [star_star] using star_mul_self (star x)"
}
] | [
94,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Order/Basic.lean | Filter.map_neg_eq_comap_neg | [] | [
1950,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1948,
1
] |
Mathlib/GroupTheory/Commutator.lean | one_mem_commutatorSet | [] | [
258,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_subset_preimage_fst | [] | [
238,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic.monic | [
{
"state_after": "n : ℕ\nR : Type u_1\ninst✝ : Ring R\n⊢ Monic (map (Int.castRingHom R) (cyclotomic n ℤ))",
"state_before": "n : ℕ\nR : Type u_1\ninst✝ : Ring R\n⊢ Monic (cyclotomic n R)",
"tactic": "rw [← map_cyclotomic_int]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nR : Type ... | [
324,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iSup_sub | [] | [
2405,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2403,
1
] |
Std/Data/Array/Lemmas.lean | Array.getElem_mem_data | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ni : Nat\na : Array α\nh : i < size a\n⊢ a[i] ∈ a.data",
"tactic": "simp [getElem_eq_data_get, List.get_mem]"
}
] | [
54,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
53,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | IsScalarTower.Algebra.ext | [
{
"state_after": "R : Type u\nS✝ : Type v\nA✝ : Type w\nB : Type u₁\nM : Type v₁\ninst✝¹² : CommSemiring R\ninst✝¹¹ : CommSemiring S✝\ninst✝¹⁰ : Semiring A✝\ninst✝⁹ : Semiring B\ninst✝⁸ : Algebra R S✝\ninst✝⁷ : Algebra S✝ A✝\ninst✝⁶ : Algebra S✝ B\ninst✝⁵ : Algebra R A✝\ninst✝⁴ : Algebra R B\ninst✝³ : IsScalarT... | [
116,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_le_rpow_of_exponent_ge | [
{
"state_after": "case intro\ny z : ℝ\nhyz : z ≤ y\nx : ℝ≥0\nhx1 : ↑x ≤ 1\n⊢ ↑x ^ y ≤ ↑x ^ z",
"state_before": "x : ℝ≥0∞\ny z : ℝ\nhx1 : x ≤ 1\nhyz : z ≤ y\n⊢ x ^ y ≤ x ^ z",
"tactic": "lift x to ℝ≥0 using ne_of_lt (lt_of_le_of_lt hx1 coe_lt_top)"
},
{
"state_after": "case pos\ny z : ℝ\nhyz : z ... | [
636,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.ind | [] | [
114,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
11
] |
Mathlib/Data/Complex/Exponential.lean | Real.quadratic_le_exp_of_nonneg | [
{
"state_after": "x✝ y x : ℝ\nhx : 0 ≤ x\n⊢ x ^ 2 / 2 = x ^ 2 / (1 + 1)",
"state_before": "x✝ y x : ℝ\nhx : 0 ≤ x\n⊢ 1 + x + x ^ 2 / 2 = ∑ i in range 3, x ^ i / ↑i !",
"tactic": "simp [Finset.sum_range_succ]"
},
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\nhx : 0 ≤ x\n⊢ x ^ 2 / ... | [
1477,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1474,
1
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_dvd | [
{
"state_after": "i j k : ℤ\n⊢ i ∣ k → j ∣ k → ↑(Nat.lcm (natAbs i) (natAbs j)) ∣ k",
"state_before": "i j k : ℤ\n⊢ i ∣ k → j ∣ k → ↑(lcm i j) ∣ k",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "i j k : ℤ\nhi : i ∣ k\nhj : j ∣ k\n⊢ ↑(Nat.lcm (natAbs i) (natAbs j)) ∣ k",
"state_before": "i j ... | [
498,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.map_zero | [] | [
707,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_iff_eq_or_eq | [] | [
80,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.intersecting_insert | [] | [
81,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.eq_ite | [
{
"state_after": "case inl\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3605350\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_4\ndec_ι : DecidableEq ι\nG : ι → Type u_3\ninst✝¹ : ... | [
2009,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2005,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_mk_subset | [] | [
1108,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.doset_union_leftCoset | [
{
"state_after": "case h\nG : Type u_1\ninst✝¹ : Group G\nα : Type ?u.64712\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na x : G\n⊢ (x ∈ ⋃ (h : { x // x ∈ H }), leftCoset (↑h * a) ↑K) ↔ x ∈ doset a ↑H ↑K",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.64712\ninst✝ : Mul α\nJ : Sub... | [
197,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.closedComplemented_iff_has_closed_compl | [] | [
137,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.coprod_inl_inr | [] | [
663,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Logic/Basic.lean | Or.elim3 | [] | [
346,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.merge_aux | [
{
"state_after": "case nil\nα : Type u_1\ninst✝ : Preorder α\nl r✝ : Ordnode α\no₁✝ : WithBot α\no₂✝ : WithTop α\nhl✝ : Valid' o₁✝ l o₂✝\nhr✝ : Valid' o₁✝ r✝ o₂✝\nsep✝ : All (fun x => All (fun y => x < y) r✝) l\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhl : Valid' o₁ nil o₂\nhr : Valid' o₁ r o₂\nsep : All... | [
1497,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.subset_closure | [] | [
270,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.constantCoeff_comp_C | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/LinearAlgebra/FinsuppVectorSpace.lean | Finset.sum_single_ite | [
{
"state_after": "R : Type u_1\nM : Type ?u.93176\nn : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\na : R\ni : n\n⊢ (Finset.sum Finset.univ fun x => Finsupp.single i a) = Finsupp.single i a\n\ncase w\nR : Type u_1\nM : Type ?u.93176\nn ... | [
167,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fin.image_castSucc | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.103387\nβ : Type ?u.103390\nγ : Type ?u.103393\nn : ℕ\n⊢ image (↑castSucc) univ = {last n}ᶜ",
"tactic": "rw [← Fin.succAbove_last, Fin.image_succAbove_univ]"
}
] | [
827,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_between | [] | [
791,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | OrderIso.coe_toHomeomorph_symm | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLeast_pair | [] | [
1008,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Deprecated/Submonoid.lean | Monoid.subset_closure | [] | [
312,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_of_op_norm_le | [] | [
219,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.refl_apply | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.limNthHom_mul | [] | [
606,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_transpose_apply | [] | [
753,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_C_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\nha : a ≠ 0\n⊢ roots (↑C a * p) = roots p",
"tactic": "by_cases hp : p = 0 <;>\n simp only [roots_mul, *, Ne.def, mul_eq_zero, C_eq_zero, or_self_iff,... | [
677,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/CategoryTheory/Endomorphism.lean | CategoryTheory.Aut.Aut_inv_def | [] | [
157,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.dual | [] | [
224,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Sign.lean | SignType.self_eq_neg_iff | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ a = -a ↔ a = 0",
"tactic": "cases a <;> decide"
}
] | [
225,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_bit1 | [] | [
287,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
11
] |
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