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/GroupTheory/NoncommPiCoprod.lean | MonoidHom.injective_noncommPiCoprod_of_independent | [
{
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"state_before": "G : Type u_2\ninst✝¹ : Group G\nι : Type u_1\nhdec : DecidableEq ι\nhfin : Fintype ι\nH : ι → Type u_3\ninst✝ : (i : ι) → Group (H i)\nϕ : (i : ι) → H i →* G\nhcomm : ∀ (i j : ι), i ≠ j → ∀ (x : H i) (y : H j), Commute (↑(ϕ i) x) (↑(ϕ j) y)\nf g : (i : ι) → H i\... | [
234,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.uncurryRight_apply | [] | [
1359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1356,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_mul_mk | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | piecewise_ae_eq_restrict | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4290136\nδ : Type ?u.4290139\nι : Type ?u.4290142\nR : Type ?u.4290145\nR' : Type ?u.4290148\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t : Set α\nf g : α → β\nhs : MeasurableSet s\n⊢ piecewise s f g =ᶠ[ae μ ⊓ 𝓟 s] f",
"state_before"... | [
4613,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4611,
1
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Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.addSalemSpencer_sphere | [
{
"state_after": "α : Type ?u.454879\nβ : Type ?u.454882\nn d k N : ℕ\nx : Fin n → ℕ\nf : (Fin n → ℕ) →+ EuclideanSpace ℝ (Fin n) :=\n { toZeroHom := { toFun := fun f => Nat.cast ∘ f, map_zero' := (_ : (fun f => Nat.cast ∘ f) 0 = 0) },\n map_add' :=\n (_ :\n ∀ (x x_1 : Fin n → ℕ),\n Zer... | [
182,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
8
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_injective | [
{
"state_after": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\n⊢ Function.Injective (ofFractionRing ∘ ↑(algebraMap K[X] (FractionRing K[X])))",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\n⊢ Function.Injective ↑(algebraMap K[X] (RatFunc K))",
"tactic": "rw [← ofFractionR... | [
918,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
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Mathlib/Init/Data/Sigma/Basic.lean | Sigma.eq | [] | [
18,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
16,
11
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_bot | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | PrincipalIdealRing.isMaximal_of_irreducible | [
{
"state_after": "case mk.intro\nR : Type u\nM : Type v\ninst✝¹ : CommRing R\ninst✝ : IsPrincipalIdealRing R\np : R\nhp : Irreducible p\na : R\nhI : span R {p} < span R {a}\n⊢ span R {a} = ⊤",
"state_before": "R : Type u\nM : Type v\ninst✝¹ : CommRing R\ninst✝ : IsPrincipalIdealRing R\np : R\nhp : Irreducib... | [
260,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulActionHom.toQuotient_apply | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_sup_closure_right | [] | [
451,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.uniformity_dist' | [
{
"state_after": "case a\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\ns : Set (Completion α × Completion α)\n⊢ s ∈ 𝓤 (Completion α) ↔ s ∈ ⨅ (ε : { ε // 0 < ε }), 𝓟 {p | dist p.fst p.snd < ↑ε}",
"state_before": "α : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\n⊢ 𝓤 (Completion α) = ⨅ (ε : { ε ... | [
164,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.trim_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3496189\nγ : Type ?u.3496192\nδ : Type ?u.3496195\nι : Type ?u.3496198\nR : Type ?u.3496201\nR' : Type ?u.3496204\ninst✝ : MeasurableSpace α\nμ : Measure α\n⊢ trim μ (_ : inst✝ ≤ inst✝) = μ",
"tactic": "simp [Measure.trim]"
}
] | [
4356,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4355,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueSet_mono | [] | [
266,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Std/Data/String/Lemmas.lean | String.findAux_of_valid | [
{
"state_after": "p : Char → Bool\nl r : List Char\n⊢ (if h : { byteIdx := utf8Len l } < { byteIdx := utf8Len l + utf8Len [] } then\n if p (get { data := l ++ [] ++ r } { byteIdx := utf8Len l }) = true then { byteIdx := utf8Len l }\n else\n let_fun this :=\n (_ :\n { byteIdx... | [
334,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
322,
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] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.bind_covering | [] | [
175,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Image.lean | Set.disjoint_image_of_injective | [] | [
1593,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1591,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.mem_map_of_mem | [] | [
717,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.le_trim | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\n⊢ ∀ (s : Set α), ↑m s ≤ extend (fun s x => ↑m s) s\n\nα : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\n⊢ extend (fun s x => ↑m s) ∅ = 0",
"state_before": "α : Type u_1\ninst✝ : MeasurableSpace α\nm : OuterMeasure α\n⊢... | [
1611,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Order/CompleteLattice.lean | le_iSup_inf_iSup | [] | [
1941,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1940,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mapDomain_one | [
{
"state_after": "no goals",
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"tactic": "simp_... | [
1550,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.union | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\n𝕝 : Type ?u.2354\nE : Type u_2\nι : Sort ?u.2360\nκ : ι → Sort ?u.2365\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns t u v A B : Set E\nhv : Absorbs 𝕜 s v\na : ℝ\nha : 0 < a\nhu : ∀ (a_1 : 𝕜), a ≤ ‖a_1‖ → u ⊆ a_1 • s\n⊢ Absorbs 𝕜 s (u ∪ v)",
"state_... | [
90,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.ofExact_obj | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.homotopicRel_empty | [] | [
707,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
9
] |
Mathlib/Data/PEquiv.lean | PEquiv.isSome_symm_get | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\na : α\nh : isSome (↑f a) = true\n⊢ ↑(PEquiv.symm f) (Option.get (↑f a) h) = some a",
"tactic": "rw [f.eq_some_iff, some_get]"
}
] | [
323,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.comap_leq_ker_subToSupQuotient | [
{
"state_after": "R : Type u_1\nM : Type u_2\nM₂ : Type ?u.39830\nM₃ : Type ?u.39833\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M₂\ninst✝³ : AddCommGroup M₃\ninst✝² : Module R M\ninst✝¹ : Module R M₂\ninst✝ : Module R M₃\nf : M →ₗ[R] M₂\np p' : Submodule R M\n⊢ comap (Submodule.subtype p) ... | [
77,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.interior_eq | [] | [
302,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsRat.to_raw_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : ℤ\nd : ℕ\ninst✝ : DivisionRing α\ninv : Invertible ↑d\n⊢ ↑n * ⅟↑d = Rat.rawCast n d",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
163,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.nextCoeff_C_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝ : Semiring R\nc : R\n⊢ (if natDegree (↑C c) = 0 then 0 else coeff (↑C c) (natDegree (↑C c) - 1)) = 0",
"state_before": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝ : Semiring R\nc : R\n⊢ nextCoeff (↑C c) = 0",
"tactic": "rw ... | [
568,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | IsometryEquiv.constSMul_symm | [] | [
175,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_multiset_prod | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_sub_le_mul_sub_of_deriv_le | [] | [
884,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.eq_natDegree_of_le_mem_support | [] | [
111,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Chain.lean | isChain_univ_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3513\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na✝ b✝ x y : α\nh : IsChain r univ\na b : α\n⊢ r a b ∨ a = b ∨ r b a",
"state_before": "α : Type u_1\nβ : Type ?u.3513\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\n⊢ IsChain r univ ↔ IsTrichotomous α r",
... | [
101,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioo_ae_eq_Ioc | [] | [
3340,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3339,
1
] |
Std/Data/List/Lemmas.lean | List.filter_cons_of_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\na : α\nl : List α\npa : p a = true\n⊢ filter p (a :: l) = a :: filter p l",
"tactic": "rw [filter, pa]"
}
] | [
1109,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1108,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.KernelFork.ι_ofι | [] | [
106,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_lpBcfₗᵢ_symm | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Submodule.exists_isCompl | [] | [
1589,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1587,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.coe_mem_source | [] | [
230,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | DirectSum.toAddMonoidAlgebra_of | [] | [
97,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_univ | [] | [
498,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.radius_neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.274675\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedS... | [
354,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Init/Logic.lean | if_ctx_congr_prop | [] | [
382,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.exists_of_LiftRel_right | [] | [
1142,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Analysis/VonNeumannAlgebra/Basic.lean | VonNeumannAlgebra.commutant_commutant | [] | [
146,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.dropFun_splitFun | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.prev_mem | [
{
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"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns : Cycle α\nhs : Nodup s\nx : α\nhx : x ∈ s\n⊢ prev s hs x hx ∈ s",
"... | [
878,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
src/lean/Init/WF.lean | Nat.caseStrongInductionOn | [] | [
183,
65
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
175,
11
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.mono_of_kernel_ι_eq_zero | [] | [
332,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.fromLocalizedModule'_smul | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type ?u.645266\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : IsL... | [
762,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Std/Data/List/Lemmas.lean | List.filter_cons_of_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\na : α\nl : List α\npa : ¬p a = true\n⊢ filter p (a :: l) = filter p l",
"tactic": "rw [filter, eq_false_of_ne_true pa]"
}
] | [
1112,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1111,
9
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.zeroSection | [
{
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518,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | nhds_eq_nhds_emetric_ball | [] | [
1392,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.ae_withDensity_iff_ae_restrict | [
{
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1721,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1717,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_zero_right | [] | [
433,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_rpow_add_lt_top_of_lintegral_rpow_lt_top | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\nhf_top : (∫⁻ (a : α), f a ^ p ∂μ) < ⊤\nhg_top : (∫⁻ (a : α), g a ^ p ∂μ) < ⊤\nhp1 : 1 ≤ p\nhp0_lt : 0 < p\n⊢ (∫⁻ (a : α), (f + g) a ^ p ∂μ) < ⊤",
"state_before": "α : Type u_1\... | [
216,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.xgcd_zero_left | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\ns t r' s' t' : R\n⊢ (let r := 0;\n fun s t r' s' t' =>\n if _hr : r = 0 then (r', s', t')\n else\n let q := r' / r;\n xgcdAux (r' % r) (s' - q * s) (t' - q * t) r s t)\n s t r' s' t' =\n (r', s'... | [
239,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/Order/WithBot.lean | WithBot.ofDual_lt_ofDual_iff | [] | [
1039,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_nat_mul_two_pi_sub_pi | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ cos (↑n * (2 * ↑π) - ↑π) = -1",
"tactic": "simpa only [cos_zero] using (cos_periodic.nat_mul n).sub_antiperiod_eq cos_antiperiodic"
}
] | [
1272,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
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src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.run_lift | [] | [
54,
167
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
54,
9
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.comp_coconePointUniqueUpToIso_hom | [] | [
799,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_liminf_of_le | [] | [
558,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.mul_one | [
{
"state_after": "no goals",
"state_before": "a : Rat\n⊢ a * 1 = a",
"tactic": "simp [mul_def, normalize_self]"
}
] | [
263,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
263,
19
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.aefinStronglyMeasurable_zero | [] | [
1144,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | norm_expSeries_summable_of_mem_ball | [] | [
201,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.rfind | [
{
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575,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ind | [
{
"state_after": "case h\nC : Type u₁\ninst✝¹ : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝ : Category D\nX : C\np : Subobject X → Prop\nh : ∀ ⦃A : C⦄ (f : A ⟶ X) [inst : Mono f], p (mk f)\nP : Subobject X\n⊢ ∀ (a : MonoOver X), p (Quotient.mk'' a)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX✝ Y Z ... | [
126,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
11
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.IsFixedPt.iterate | [] | [
68,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/Data/Set/Accumulate.lean | Set.iUnion_accumulate | [
{
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57,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_smul_le | [
{
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277,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.sigma_of_hasSum | [
{
"state_after": "no goals",
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423,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_eq_set_indicator | [
{
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323,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.noncommProd_mem | [
{
"state_after": "case h\nM : Type u_1\nA : Type ?u.31592\nB : Type ?u.31595\ninst✝² : Monoid M\ninst✝¹ : SetLike B M\ninst✝ : SubmonoidClass B M\nS✝ : B\ns S : Submonoid M\nι : Type u_2\nt : Finset ι\nf : ι → M\ncomm : Set.Pairwise ↑t fun a b => Commute (f a) (f b)\nh : ∀ (c : ι), c ∈ t → f c ∈ S\n⊢ ∀ (x : M),... | [
182,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | right_subset_compRel | [] | [
194,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Int/Basic.lean | Int.sign_coe_nat_of_nonzero | [] | [
281,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | Antitone.mul_monotone | [] | [
443,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.length_ofList | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Part.lean | Part.mul_def | [] | [
699,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_commonNeighbors_top | [
{
"state_after": "ι : Sort ?u.303485\n𝕜 : Type ?u.303488\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\ninst✝¹ : Fintype V\ninst✝ : DecidableEq V\nv w : V\nh : v ≠ w\n⊢ card (Set.toFinset Set.univ \\ Set.toFinset {v, w}) = Fintype.card V - 2",
"st... | [
1637,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1632,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.nonpos_of_restrict_le_zero | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.585667\nm : MeasurableSpace α\nM : Type u_2\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\nv w : VectorMeasure α M\ni j : Set α\nhi₂ : restrict v i ≤ restrict 0 i\nhi₁ : MeasurableSet i\n⊢ ↑v i ≤ 0\n\ncase neg\nα : Type u_1\nβ : Type ?u.585667... | [
1006,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym_singleton | [] | [
183,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.isCompact_closure_image_closedBall | [] | [
165,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.seq_mem_seq | [] | [
2630,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2628,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.smul_integral_comp_sub_mul | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14928733\n𝕜 : Type ?u.14928736\nE : Type u_1\nF : Type ?u.14928742\nA : Type ?u.14928745\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d✝ : ℝ\nf : ℝ → E\nc d : ℝ\n⊢ (c • ∫ (x : ℝ) in a..b, f (d - c * x)) =... | [
823,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.apply_clm | [] | [
85,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.308656\ninst✝¹ : PseudoEMetricSpace α\nγ : Type w\ninst✝ : EMetricSpace γ\nx y : γ\n⊢ 0 < edist x y ↔ x ≠ y",
"tactic": "simp [← not_le]"
}
] | [
1019,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ico | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na b : α i\n⊢ update f i '' Ico a b = Ico (update f i a) (update f i b)",
"tactic": "rw [← Icc_diff_right, ← Icc_diff_right, image_diff (up... | [
148,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm_of_integrable | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.411774\nF' : Type u_3\nG : Type ?u.411780\n𝕜 : Type ?u.411783\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
604,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Logic/Unique.lean | Unique.eq_default | [] | [
146,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_iUnion | [] | [
240,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.smul_re | [] | [
365,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_sub_nat_mul_two_pi | [] | [
1185,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/Data/ULift.lean | ULift.up_injective | [] | [
101,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_le | [] | [
95,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.825109\nγ : Type ?u.825112\nδ : Type ?u.825115\nι : Type ?u.825118\nR : Type ?u.825121\nR' : Type ?u.825124\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν✝ ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nμ ν : Measure α\ninst✝¹ : ... | [
3872,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3862,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulDysonEtransform.subset | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CommGroup α\ne : α\nx : Finset α × Finset α\n⊢ e • x.snd * e⁻¹ • x.fst ⊆ x.fst * x.snd",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : CommGroup α\ne : α\nx : Finset α × Finset α\n⊢ (mulDysonEtransform e x).fst * (mulDysonEtran... | [
64,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_def | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Order/Basic.lean | OrderDual.partialOrder.dual_dual | [] | [
738,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mk_le_mk | [] | [
229,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
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