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/LinearAlgebra/Prod.lean | LinearMap.tailing_le_tunnel | [
{
"state_after": "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.536871\nM₆ : Type ?u.536874\ninst✝⁴ : Ring R\nN : Type u_1\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf... | [
938,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.140286\nι : Sort x\nf : Filter α\nt : NeBot f\np : Prop\nh : p\n⊢ (∀ᶠ (x : α) in f, p) ↔ p",
"tactic": "simp [h]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\... | [
1112,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Data/List/Sigma.lean | List.kerase_nil | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Std/Data/List/Lemmas.lean | List.isSuffix.isInfix | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ : List α✝\nx✝ : l₁ <:+ l₂\nt : List α✝\nh : t ++ l₁ = l₂\n⊢ t ++ l₁ ++ [] = l₂",
"tactic": "rw [h, append_nil]"
}
] | [
1570,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1570,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Comonad.coalgebra_iso_of_iso | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nG : Comonad C\nA B : Coalgebra G\nf : A ⟶ B\ninst✝ : IsIso f.f\n⊢ A.a ≫ G.map f.f ≫ G.map (inv f.f) = A.a",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nG : Comonad C\nA B : Coalgebra G\nf : A ⟶ B\ninst✝ : IsIso f.f\n⊢ B.a ≫ G.map (inv f.f) = inv f.f... | [
495,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.trans_left | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.18673\nγ : Type ?u.18676\nδ : Type ?u.18679\nr : α → α → Prop\na b c d : α\nhab : TransGen r a b\n⊢ TransGen r a b\n\ncase tail\nα : Type u_1\nβ : Type ?u.18673\nγ : Type ?u.18676\nδ : Type ?u.18679\nr : α → α → Prop\na b c d : α\nhab : TransGen r a b\nb✝ c... | [
361,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_X | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nthis : X = ↑(monomial 1) 1\n⊢ ↑toLaurent X = T 1",
"state_before": "R : Type u_1\ninst✝ : Semiring R\n⊢ ↑toLaurent X = T 1",
"tactic": "have : (Polynomial.X : R[X]) = monomial 1 1 := by simp [← C_mul_X_pow_eq_monomial]"
},
{
"state_after": "no ... | [
229,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Balanced.balRight | [
{
"state_after": "α✝ : Type u_1\nl : RBNode α✝\nv : α✝\nr : RBNode α✝\ncl : RBColor\nn : Nat\nhl : Balanced l cl (n + 1)\nhr : RedRed True r n\n⊢ RedRed (cl = red)\n (match r with\n | node red b y c => node red l v (node black b y c)\n | r =>\n match l with\n | node black a x b => balance1 (n... | [
301,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
287,
11
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Ico_right | [] | [
456,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic'_ne_zero | [] | [
107,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.extendDomain_mul | [] | [
321,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.nat_sqrt_le_real_sqrt | [
{
"state_after": "a : ℕ\n⊢ ↑(Nat.sqrt a) ^ 2 ≤ ↑a",
"state_before": "a : ℕ\n⊢ ↑(Nat.sqrt a) ≤ sqrt ↑a",
"tactic": "rw [Real.le_sqrt (Nat.cast_nonneg _) (Nat.cast_nonneg _)]"
},
{
"state_after": "a : ℕ\n⊢ Nat.sqrt a ^ 2 ≤ a",
"state_before": "a : ℕ\n⊢ ↑(Nat.sqrt a) ^ 2 ≤ ↑a",
"tactic": "n... | [
457,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | groupoid_of_pregroupoid_le | [
{
"state_after": "H : Type u\nH' : Type ?u.32686\nM : Type ?u.32689\nM' : Type ?u.32692\nM'' : Type ?u.32695\ninst✝ : TopologicalSpace H\nPG₁ PG₂ : Pregroupoid H\nh : ∀ (f : H → H) (s : Set H), Pregroupoid.property PG₁ f s → Pregroupoid.property PG₂ f s\ne : LocalHomeomorph H H\nhe : e ∈ Pregroupoid.groupoid PG... | [
356,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.st_mul | [] | [
657,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.add_coeff_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nx y : 𝕎 R\n⊢ coeff (x + y) 0 = coeff x 0 + coeff y 0",
"tactic": "simp [add_coeff, peval]"
}
] | [
390,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.inv | [] | [
94,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.sizeOf_lt_sizeOf_of_mem | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.137282\nγ : Type ?u.137285\ninst✝ : SizeOf α\nx : α\ns : Multiset α\nhx✝ : x ∈ s\nl : List α\nhx : x ∈ Quot.mk Setoid.r l\n⊢ SizeOf.sizeOf x < SizeOf.sizeOf (Quot.mk Setoid.r l)",
"state_before": "α : Type u_1\nβ : Type ?u.137282\nγ : Type ?u.137285\ninst✝... | [
1509,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
1
] |
Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9087\na : α\ns : Multiset α\nl : List α\n⊢ zip (powersetAux' l ++ List.map (cons a) (powersetAux' l))\n (reverse (List.map (cons a) (powersetAux' l)) ++ reverse (powersetAux' l)) ~\n List.map (fun x => Prod.map id (cons a) x) (zip (powersetAux' l) (reverse (po... | [
88,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Category/Ring/Instances.lean | isLocalRingHom_of_iso | [
{
"state_after": "case h.e'_3\nR S : CommRingCat\nf : R ≅ S\na : ↑R\nha : IsUnit (↑f.hom a)\n⊢ a = ↑f.inv (↑f.hom a)",
"state_before": "R S : CommRingCat\nf : R ≅ S\na : ↑R\nha : IsUnit (↑f.hom a)\n⊢ IsUnit a",
"tactic": "convert f.inv.isUnit_map ha"
},
{
"state_after": "no goals",
"state_be... | [
58,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_sub | [] | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.ext_iff | [] | [
1470,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_def | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y : C\nf g : X ⟶ Y\nH : C\nh : H ⟶ X\nhG : IsSeparator H\nhfg : ∀ (h : H ⟶ X), h ≫ f = h ≫ g\nhH : H ∈ {H}\n⊢ h ≫ f = h ≫ g",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nG : C\nhG :... | [
462,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.neg_vecMul | [
{
"state_after": "case h\nl : Type ?u.907608\nm : Type u_1\nn : Type u_2\no : Type ?u.907617\nm' : o → Type ?u.907622\nn' : o → Type ?u.907627\nR : Type ?u.907630\nS : Type ?u.907633\nα : Type v\nβ : Type w\nγ : Type ?u.907640\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : Fintype m\nv : m → α\nA : Matrix m n α\nx✝... | [
1898,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1896,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.mem_map_iff_mem | [] | [
263,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_injective | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\na✝ b : Γ\nr✝ : R\na : Γ\nr s : R\nrs : ↑(single a) r = ↑(single a) s\n⊢ r = s",
"tactic": "rw [← single_coeff_same a r, ← single_coeff_same a s, rs]"
}
] | [
192,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_surjective | [] | [
137,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.lt_nfpFamily | [] | [
75,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.map_vadd_multiples | [
{
"state_after": "case mk.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.136331\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddCommMonoid α\nhf : Periodic f c\nx : α\nm : ℕ\n⊢ f ({ val := (fun i => i • c) m, property := (_ : ∃ y, (fun i => i • c) y = (fun i => i • c) m) } +ᵥ x) = f x",
"state_before": "α : Type u... | [
341,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_norm_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.119592\nE : Type u_2\nF : Type ?u.119598\nG : Type ?u.119601\nE' : Type ?u.119604\nF' : Type u_3\nG' : Type ?u.119610\nE'' : Type ?u.119613\nF'' : Type ?u.119616\nG'' : Type ?u.119619\nR : Type ?u.119622\nR' : Type ?u.119625\n𝕜 : Type ?u.119628\n𝕜' : Type ?u.119631\... | [
716,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae | [
{
"state_after": "α : Type u_1\nι : Type ?u.20960\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : MetricSpace E\nf : ℕ → α → E\ng : α → E\nhfg : TendstoInMeasure μ f atTop g\nh_lt_ε_real : ∀ (ε : ℝ), 0 < ε → ∃ k, 2 * 2⁻¹ ^ k < ε\n⊢ ∃ ns, StrictMono ns ∧ ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) ... | [
245,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_eq_max_sub_min | [
{
"state_after": "i j : ℕ\nh : i < j\n⊢ dist i j = max i j - min i j",
"state_before": "i j : ℕ\n⊢ i < j → dist i j = max i j - min i j",
"tactic": "intro h"
},
{
"state_after": "no goals",
"state_before": "i j : ℕ\nh : i < j\n⊢ dist i j = max i j - min i j",
"tactic": "rw [max_eq_right_... | [
114,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformEmbedding_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.62248\nι : Type ?u.62251\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝ : PseudoMetricSpace β\nf : α → β\n⊢ UniformEmbedding f ↔\n Function.Injective f ∧\n UniformContinuous f ∧ ∀ (δ : ℝ), δ ... | [
846,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
8
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjectionFn_norm_sq | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.463344\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nv : E\np : E := orthogonalProjectionFn K... | [
438,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_const_vadd_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.117591\nP : Type u_3\nP' : Type ?u.117597\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx y z : P\n... | [
214,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Analysis/Calculus/FDerivSymmetric.lean | second_derivative_symmetric_of_eventually | [
{
"state_after": "case intro.intro\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf✝ : E → F\nf'✝ : E → E →L[ℝ] F\nf''✝ : E →L[ℝ] E →L[ℝ] F\nhf✝ : ∀ (x : E), x ∈ interior s → HasFDerivA... | [
319,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.measure_diff_left | [] | [
134,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.comap_cobounded_le | [] | [
389,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.comap_cocompact_le | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.89720\nπ : ι → Type ?u.89725\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nf : α → β\nhf : Continuous f\n⊢ ∀ (i' : Set α), IsCompact i' → ∃ i, IsCompact i ∧ f ⁻¹' iᶜ ⊆ i'ᶜ",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.89... | [
844,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_mono | [] | [
812,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nh : Tendsto (fun x => eval x P) atTop atTop\n⊢ 0 < degree P ∧ 0 ≤ leadingCoeff P",
"state_before": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\n⊢ Tend... | [
73,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mapEquiv_refl | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type ?u.654570\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.655023\ninst✝¹ : Co... | [
839,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_rpow | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\n⊢ log b ≠ 0",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\n⊢ logb b (b ^ x) = x",
"tactic": "rw [logb, div_eq_iff, log_rpow b_pos]"
},
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_ne_on... | [
92,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | dvd_add_self_left | [] | [
140,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.next | [
{
"state_after": "case refl\nl : List Char\nc : Char\nr : List Char\nh : ValidFor l (c :: r) { s := { data := List.reverse l ++ c :: r }, i := { byteIdx := utf8Len (List.reverse l) } }\n⊢ ValidFor (c :: l) r\n (Iterator.next { s := { data := List.reverse l ++ c :: r }, i := { byteIdx := utf8Len (List.reverse... | [
552,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
548,
1
] |
Mathlib/Data/String/Basic.lean | String.Iterator.hasNext_cons_addChar | [
{
"state_after": "no goals",
"state_before": "c : Char\ncs : List Char\ni : Pos\n⊢ hasNext { s := { data := c :: cs }, i := i + c } = hasNext { s := { data := cs }, i := i }",
"tactic": "simp [hasNext, Nat.add_lt_add_iff_lt_right]"
}
] | [
25,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.stabilizer_of_subMul | [
{
"state_after": "S : Type u'\nT : Type u''\nR : Type u\nM : Type v\ninst✝¹ : Group R\ninst✝ : MulAction R M\np : SubMulAction R M\nm : { x // x ∈ p }\n⊢ (MulAction.stabilizer R m).toSubmonoid = (MulAction.stabilizer R ↑m).toSubmonoid",
"state_before": "S : Type u'\nT : Type u''\nR : Type u\nM : Type v\nins... | [
323,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | DifferentiableWithinAt.arctan | [] | [
195,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.integrable_indicator | [] | [
268,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.map_of | [] | [
570,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_inter | [] | [
1598,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1597,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioc_of_interval_integral_norm_bounded_right | [] | [
614,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.SupHom.apply_blimsup_le | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nι : Type ?u.152425\ninst✝¹ : CompleteLattice α\nf g✝ : Filter β\np q : β → Prop\nu v : β → α\ninst✝ : CompleteLattice γ\ng : sSupHom α γ\n⊢ ↑g (⨅ (s : Set β) (_ : s ∈ f), ⨆ (b : β) (_ : p b ∧ b ∈ s), u b) ≤\n ⨅ (s : Set β) (_ : s ∈ f), ⨆ (b : β) (_ ... | [
966,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.eventually_smallSets | [] | [
71,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_add | [
{
"state_after": "case zero\nι : Type ?u.441582\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\nn : ℕ\n⊢ ∏ x in range (n + Nat.zero), f x = (∏ x in range n, f x) * ∏ x in range Nat.zero, f (n + x)\n\ncase succ\nι : Type ?u.441582\nβ : Type u\nα : Ty... | [
1249,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
] |
Mathlib/RingTheory/SimpleModule.lean | LinearMap.surjective_of_ne_zero | [] | [
151,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Topology/Covering.lean | isCoveringMap_iff_isCoveringMapOn_univ | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace E\ninst✝ : TopologicalSpace X\nf : E → X\ns : Set X\n⊢ IsCoveringMap f ↔ IsCoveringMapOn f Set.univ",
"tactic": "simp only [IsCoveringMap, IsCoveringMapOn, Set.mem_univ, forall_true_left]"
}
] | [
144,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.measurable_coe | [] | [
214,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
11
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Affine.Simplex.span_eq_top | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type ?u.206684\nι : Type ?u.206687\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : FiniteDimensional k V\nn : ℕ\nT : Simplex k V n\nhrank : finrank k V = n\n⊢ affineSpan k ... | [
280,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.liftRel_think_right | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nca : Computation α\ncb : Computation β\n⊢ LiftRel (swap R) (think cb) ca ↔ LiftRel (swap R) cb ca",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nca : Computation α\ncb : Computation β\n⊢ LiftRel R ca (think cb)... | [
1211,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.zero | [] | [
115,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.symm_toEquiv_eq_symm | [] | [
341,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.injective_iff_bijective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27086\nγ : Type ?u.27089\ninst✝ : Finite α\nf : α → α\n⊢ Injective f ↔ Bijective f",
"tactic": "simp [Bijective, injective_iff_surjective]"
}
] | [
634,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.openSegment_subset | [] | [
75,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Embedding.apply_mem_neighborSet_iff | [] | [
1786,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_log_of_pos | [] | [
491,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_prod_X_sub_C_iff | [
{
"state_after": "no goals",
"state_before": "F : Type u\ninst✝² : Field F\nK : Type v\ninst✝¹ : Field K\nι : Type u_1\ninst✝ : Fintype ι\nf : ι → F\n⊢ (∀ (x : ι), x ∈ univ → ∀ (y : ι), y ∈ univ → f x = f y → x = y) ↔ Function.Injective f",
"tactic": "simp_rw [mem_univ, true_imp_iff, Function.Injective]... | [
309,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.cutMap_nonempty | [] | [
144,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_lt_of_right_le | [] | [
322,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.mass_zero_iff | [
{
"state_after": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nμ : FiniteMeasure Ω\nμ_mass : mass μ = 0\n⊢ μ = 0",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nμ : FiniteMeasure Ω\n⊢ mass μ = 0 ↔ μ = 0",
"tactic": "refine' ⟨fun μ_mass => _, fun hμ => by simp only [hμ, zero_mass]⟩"
},
{
... | [
182,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Std/Data/List/Lemmas.lean | List.diff_cons | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\n⊢ (if a ∈ l₁ then List.diff (List.erase l₁ a) l₂ else List.diff l₁ l₂) = List.diff (List.erase l₁ a) l₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\n⊢ List.diff l₁ (a :: l₂) = List.diff (List.eras... | [
1495,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1494,
9
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.toSubmonoid_mono | [] | [
473,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
src/lean/Init/Control/Lawful.lean | pure_id_seq | [
{
"state_after": "no goals",
"state_before": "f : Type u_1 → Type u_2\nα : Type u_1\ninst✝¹ : Applicative f\ninst✝ : LawfulApplicative f\nx : f α\n⊢ (Seq.seq (pure id) fun x_1 => x) = x",
"tactic": "simp [pure_seq]"
}
] | [
44,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
43,
9
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.inductionOn | [] | [
129,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Order/Directed.lean | directedOn_of_inf_mem | [] | [
166,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.centralizer_le | [] | [
1411,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.of_near | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\ng : CauSeq β abv\nh : ∀ (ε : α), ε > 0 → ∃ i, ∀ (j : ℕ), j ≥ i → abv (f j - ↑g j) < ε\nε : α\nε0 : ε > 0\ni : ℕ\nhi : ∀ (j : ℕ), j ≥ i → abv (f j - ↑g j)... | [
519,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.strictMono_x | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : m < n + 1\nthis : xn a1 m ≤ xn a1 n\n⊢ xn a1 m < xn a1 (n + 1)",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : m < n + 1\n⊢ xn a1 m < xn a1 (n + 1)",
"tactic": "have : xn a1 m ≤ xn a1 n :=\n Or.elim (lt_or_eq_of_le <| Nat.le_of_succ_le_succ h) (fun h... | [
423,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.erase | [] | [
317,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.dotProduct_vecMul_hadamard | [
{
"state_after": "α : Type u_3\nβ : Type ?u.28934\nγ : Type ?u.28937\nm : Type u_1\nn : Type u_2\nR : Type ?u.28946\nA B C : Matrix m n α\ninst✝⁶ : Fintype m\ninst✝⁵ : Fintype n\ninst✝⁴ : Semiring α\ninst✝³ : Semiring R\ninst✝² : Module R α\ninst✝¹ : DecidableEq m\ninst✝ : DecidableEq n\nv : m → α\nw : n → α\n⊢... | [
158,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Prod.segment_subset | [
{
"state_after": "case intro.intro.intro.intro.intro\n𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.301724\nι : Type ?u.301727\nπ : ι → Type ?u.301732\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y z : E × F\na b : 𝕜\nha... | [
594,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.isTopologicalBasis_opens | [
{
"state_after": "no goals",
"state_before": "α : Type u\nt : TopologicalSpace α\n⊢ ∀ (u : Set α), u ∈ {U | IsOpen U} → IsOpen u",
"tactic": "tauto"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nt : TopologicalSpace α\n⊢ ∀ (a : α) (u : Set α), a ∈ u → IsOpen u → ∃ v, v ∈ {U | ... | [
242,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\nh0 : p₁ = p₂ ∨ p₃ ≠ p₂\n⊢ Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ p₂",
"state_before": "V ... | [
489,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_one_X | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\n⊢ ↑(coeff R 1) X = 1",
"tactic": "rw [coeff_X, if_pos rfl]"
}
] | [
1441,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iSup_inf_of_monotone | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\nκ : ι✝ → Sort ?u.12298\ninst✝² : Frame α\ns t : Set α\na b : α\nι : Type u_1\ninst✝¹ : Preorder ι\ninst✝ : IsDirected ι fun x x_1 => x ≤ x_1\nf g : ι → α\nhf : Monotone f\nhg : Monotone g\n⊢ ((⨆ (i : ι), f i) ⊓ ⨆ (i : ι), g i) ≤ ⨆ (i : ι), f i ⊓ g i",
"... | [
164,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Equitabilise.lean | Finpartition.card_filter_equitabilise_small | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nm n a b : ℕ\nP : Finpartition s\nh : a * m + b * (m + 1) = card s\nhm : m ≠ 0\n⊢ card (filter (fun u => card u = m) (equitabilise h).parts) * m + b * (m + 1) = a * m + b * (m + 1)",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns... | [
188,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_disjoint_ball | [] | [
550,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_eq_sum_range' | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type ?u.1288464\nB' : Type ?u.1288467\na b : R\nn✝ : ℕ\ninst✝⁸ : CommSemiring A'\ninst✝⁷ : Semiring B'\ninst✝⁶ : CommSemiring R\np✝ q : R[X]\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\nB : Type ?u.1288680\ninst✝³ : Semiring B\ninst✝² : Algeb... | [
364,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.pointReflection_fixed_iff_of_module | [] | [
608,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_inj | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\ninst✝ : ∀ (i : ι), NeBot (f₁ i)\nh : pi f₁ = pi f₂\n⊢ f₁ = f₂",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\ninst✝ : ∀ (i : ι), NeBot (f... | [
187,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_mem_of_subset | [] | [
248,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.casesOn' | [] | [
147,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
11
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_digits | [
{
"state_after": "case zero\nn✝ n : ℕ\n⊢ ofDigits zero (digits zero n) = n\n\ncase succ\nn✝ n b : ℕ\n⊢ ofDigits (succ b) (digits (succ b) n) = n",
"state_before": "n✝ b n : ℕ\n⊢ ofDigits b (digits b n) = n",
"tactic": "cases' b with b"
},
{
"state_after": "case zero.zero\nn : ℕ\n⊢ ofDigits zero ... | [
276,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.inv_apply | [] | [
530,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.dual_right | [] | [
244,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/List/Permutation.lean | List.map_permutationsAux2 | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nt : α\nts ys : List α\nf : List α → β\n⊢ (permutationsAux2 (id t) ts (map f []) ys ?f').snd = (permutationsAux2 t ts [] ys f).snd\n\ncase f'\nα : Type u_1\nβ : Type u_2\nt : α\nts ys : List α\nf : List α → β\n⊢ List α → β\n\ncase f'\nα : Type u_1\nβ : Type u_2\nt : ... | [
108,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_inv_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ b✝ c a b : G\n⊢ a * b * b⁻¹ = a",
"tactic": "rw [mul_assoc, mul_right_inv, mul_one]"
}
] | [
1119,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Logic/Basic.lean | ball_or_left | [] | [
1109,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.108457\nβ : Type ?u.108460\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a ≠ 0 → ∀ (n : ℕ), a ^ n ≠ 0",
"tactic": "simpa only [pos_iff_ne_zero] using ENNReal.pow_pos"
}
] | [
751,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
11
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomain.quotientEquivPiFactors_mk | [] | [
1350,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.volume_subtype_coe_le_volume | [] | [
1462,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
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