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/ModelTheory/Basic.lean | FirstOrder.Language.Hom.toFun_eq_coe | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
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Mathlib/LinearAlgebra/Pi.lean | Submodule.pi_empty | [] | [
288,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePushout.hom_eq_desc | [
{
"state_after": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type ?u.254030\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → B ⟶ objs j\ninst✝ : HasWidePushout B objs arrows\nX : D\nf : B ⟶ X\nfs : (j : J) → objs j ⟶ X\nw : ∀ (j : J), arrows j ≫ fs j = f\ng : widePushout B (fun j => objs j) a... | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_ne_zero_of_finite | [
{
"state_after": "case intro\nG : Type u\ninst✝¹ : LeftCancelMonoid G\ninst✝ : Finite G\nval✝ : Fintype G\n⊢ exponent G ≠ 0",
"state_before": "G : Type u\ninst✝¹ : LeftCancelMonoid G\ninst✝ : Finite G\n⊢ exponent G ≠ 0",
"tactic": "cases nonempty_fintype G"
},
{
"state_after": "no goals",
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274,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/Data/Finset/Image.lean | Finset.image_inter | [] | [
495,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_of_one_le | [
{
"state_after": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : CommGroup α\na : α\nh : 1 ≤ a\n⊢ a ⊔ 1 = a",
"state_before": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : CommGroup α\na : α\nh : 1 ≤ a\n⊢ a⁺ = a",
"tactic": "rw [m_pos_part_def]"
},
{
"state_after": "no goals",
"state_before": "α : Type ... | [
468,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_union_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.401923\nι : Type ?u.401926\ninst✝³ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\nf g : α → β\ninst✝ : PseudoMetrizableSpace β\ns t : Set α\n⊢ AEStronglyMeasu... | [
1721,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1718,
1
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Std/Data/Array/Lemmas.lean | Array.ugetElem_eq_getElem | [] | [
45,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
44,
9
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.map_volume_mul_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2204078\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\n⊢ Measure.map (fun x => a * x) volume = ofReal (abs a⁻¹) • volume",
"tactic": "conv_rhs =>\n rw [← Real.smul_map_volume_mul_left h, smul_smul, ← ENNReal.ofReal_mul (abs_nonneg _), ←\n abs_mul, inv... | [
315,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.fg_of_fg_map | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Subalgebra R A\nf : A →ₐ[R] B\nhf : Function.Injective ↑f\nhs✝ : FG (map f S)\ns : Finset B\nhs : Algebra.adjoin R ↑s = map f S\n⊢ ↑s ⊆ Set.rang... | [
162,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_refl | [] | [
732,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.Cotrident.ofCocone_ι | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝ : Category C\nX Y : C\nf : J → (X ⟶ Y)\nF : WalkingParallelFamily J ⥤ C\nt : Cocone F\nj : WalkingParallelFamily J\n⊢ (parallelFamily fun j => F.map (line j)).obj j = F.obj j",
"tactic": "cases j <;> aesop_cat"
}
] | [
509,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/Topology/Algebra/UniformGroup.lean | TendstoUniformlyOn.div | [] | [
505,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_one | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.open_image | [
{
"state_after": "case inl\n𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.303710\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedSpace 𝕜 G\nG' : Type ... | [
335,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
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] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.subgraphOfAdj_eq_induce | [
{
"state_after": "case verts.h\nι : Sort ?u.263704\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' G'' : Subgraph G\ns s' : Set V\nv w : V\nhvw : SimpleGraph.Adj G v w\nx✝ : V\n⊢ x✝ ∈ (subgraphOfAdj G hvw).verts ↔ x✝ ∈ (induce ⊤ {v, w}).verts\n\ncase Adj.h.h.a\nι : Sort ?u.263704\nV : Type u\nW : Type v\nG : Sim... | [
1196,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_ge_inter_not_ge | [] | [
402,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/RingTheory/SimpleModule.lean | IsSemisimpleModule.sSup_simples_eq_top | [
{
"state_after": "R : Type u_2\ninst✝⁵ : Ring R\nM : Type u_1\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nm : Submodule R M\nN : Type ?u.40765\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : IsSemisimpleModule R M\n⊢ sSup {m | IsAtom m} = ⊤",
"state_before": "R : Type u_2\ninst✝⁵ : Ring R\nM : Typ... | [
113,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_one | [] | [
1094,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_prod | [] | [
287,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_le_of_le_sub_left | [] | [
462,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
461,
11
] |
Mathlib/RingTheory/FiniteType.lean | Algebra.FiniteType.of_surjective | [
{
"state_after": "case h.e'_6\nR : Type u_1\nA : Type u\nB : Type u_2\nM : Type ?u.22919\nN : Type ?u.22922\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nhRA :... | [
113,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Std/Data/Int/Lemmas.lean | Int.pos_of_neg_neg | [
{
"state_after": "no goals",
"state_before": "a : Int\nh : -a < 0\n⊢ -a < -0",
"tactic": "rwa [Int.neg_zero]"
}
] | [
888,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
887,
11
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cocone F\nX : C\nh : coyoneda.obj X.op ⋙ uliftFunctor ≅ Functor.cocones F\nY : C\nf : X ⟶ Y\n⊢ { pt := Y, ι := h.hom.app Y { down := f } } = { pt := Y, ι := h.hom.app X { down :=... | [
1032,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Order/WellFoundedSet.lean | Finset.isPwo_sup | [] | [
582,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Deprecated/Group.lean | IsMulHom.mul | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ✝ : Type v\ninst✝⁴ : Mul α✝\ninst✝³ : Mul β✝\nγ : Type ?u.931\ninst✝² : Mul γ\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Semigroup α\ninst✝ : CommSemigroup β\nf g : α → β\nhf : IsMulHom f\nhg : IsMulHom g\na b : α\n⊢ f (a * b) * g (a * b) = f a * g a * ... | [
82,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | lipschitzWith_min | [] | [
432,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_div_nat | [] | [
450,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Equiv.not_fuzzy' | [] | [
955,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_zero_right | [] | [
262,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | Subgroup.isOpen_of_mem_nhds | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : ContinuousMul G\nH : Subgroup G\ng : G\nhg : ↑H ∈ 𝓝 g\nx : G\nhx : x ∈ ↑H\n⊢ ↑H ∈ 𝓝 x",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : ContinuousMul G\nH : Subgroup G\ng : G\nhg : ... | [
318,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_land | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\nk : ℕ\n⊢ testBit (land m n) k = (testBit m k && testBit n k)",
"tactic": "rw [← bitwise_and, testBit_bitwise]"
}
] | [
351,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsSup_eq_iInf_sSup | [] | [
676,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.map_zero₂ | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_6\ninst✝¹⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.150367\ninst✝¹⁵ : NormedAddCommGroup E\ninst✝¹⁴ : NormedSpace 𝕜 E\nF : Type u_5\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : NormedSpace 𝕜 F\nG : Type ?u.150552\ninst✝¹¹ : NormedAddCommGroup G\nins... | [
301,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.cons_nil_iff_singleton | [
{
"state_after": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nx : α\nb : Bool\nh : Red ((x, b) :: L) []\nh₁ : Red ((x, !b) :: (x, b) :: L) [(x, !b)]\n⊢ Red L [(x, !b)]",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nx : α\nb : Bool\nh : Red ((x, b) :: L) []\n⊢ Red L [(x, !b)]",
"tactic"... | [
342,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.apply_of_col_ne | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.23553\nm : Type u_3\nn : Type u_1\nR : Type ?u.23562\nα : Type u_2\ninst✝³ : DecidableEq l\ninst✝² : DecidableEq m\ninst✝¹ : DecidableEq n\ninst✝ : Semiring α\ni✝ : m\nj✝ : n\nc : α\ni'✝ : m\nj'✝ : n\ni i' : m\nj j' : n\nhj : j ≠ j'\na : α\n⊢ stdBasi... | [
142,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.one | [] | [
394,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.homOfLe_ι | [
{
"state_after": "case w.h.h\nC : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG✝ G'✝ G G' : Subpresheaf F\nh : G ≤ G'\nx✝ : Cᵒᵖ\na✝ : (toPresheaf G).obj x✝\n⊢ (homOfLe h ≫ ι G').app x✝ a✝ = (ι G).app x✝ a✝",
"state_before": "C : Type u\ninst✝ : Category C\nJ : Grothendie... | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.Infinite.exists_supset_ncard_eq | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.135186\ns✝ t✝ : Set α\na b x y : α\nf : α → β\ns t : Set α\nht : Set.Infinite t\nhst : s ⊆ t\nhs : Set.Finite s\nk : ℕ\nhsk : Set.ncard s ≤ k\ns₁ : Set α\nhs₁ : s₁ ⊆ t \\ s\nhs₁fin : Set.Finite s₁\nhs₁card : Set.ncard s₁ = k - Set.ncard s\n⊢ ∃ ... | [
620,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Order/MinMax.lean | Monotone.map_max | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\nhf : Monotone f\n⊢ f (max a b) = max (f a) (f b)",
"tactic": "cases' le_total a b with h h <;> simp [h, hf h]"
}
] | [
257,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | multiplicity.Int.pow_add_pow | [
{
"state_after": "R : Type ?u.836891\nn✝ : ℕ\ninst✝ : CommRing R\na b x✝ y✝ : R\np : ℕ\nhp : Nat.Prime p\nhp1 : Odd p\nx y : ℤ\nhxy : ↑p ∣ x - -y\nhx : ¬↑p ∣ x\nn : ℕ\nhn : Odd n\n⊢ multiplicity (↑p) (x ^ n + y ^ n) = multiplicity (↑p) (x + y) + multiplicity p n",
"state_before": "R : Type ?u.836891\nn✝ : ℕ... | [
227,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_iSup | [] | [
338,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.exists_approx_preimage_norm_le | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ninst✝ : CompleteSpace F\nsurj : Surjective ↑f\nA : (⋃ (n : ℕ), closure (↑f '' ball... | [
165,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_zero | [] | [
374,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasurableEmbedding.lintegral_map | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1366326\nδ : Type ?u.1366329\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSpace β\ng : α → β\nhg : MeasurableEmbedding g\nf : β → ℝ≥0∞\n⊢ (⨆ (g_1 : β →ₛ ℝ≥0∞) (_ : ↑g_1 ≤ fun a => f a), SimpleFunc.lintegral g_1 (Measure.map g μ)) =\n ⨆ (... | [
1321,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1311,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.mk_smul | [] | [
85,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.supports_biUnion | [
{
"state_after": "K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ (∀ (q : Λ') (x : Option Γ'), q ∈ K x → TM2.SupportsStmt S (tr q)) ↔\n ∀ (a : Option Γ') (q : Λ'), q ∈ K a → TM2.SupportsStmt S (tr q)",
"state_before": "K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ Supports (Finset.biUnion Finset.univ K) S ↔ ∀ ... | [
1931,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1929,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_six | [
{
"state_after": "x : ℝ\n⊢ cos (π / 2 - π / 6) = cos (π / 3)",
"state_before": "x : ℝ\n⊢ sin (π / 6) = 1 / 2",
"tactic": "rw [← cos_pi_div_two_sub, ← cos_pi_div_three]"
},
{
"state_after": "case e_x\nx : ℝ\n⊢ π / 2 - π / 6 = π / 3",
"state_before": "x : ℝ\n⊢ cos (π / 2 - π / 6) = cos (π / 3)... | [
893,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/RingTheory/DedekindDomain/PID.lean | FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_top | [
{
"state_after": "R✝ : Type ?u.9292\ninst✝⁴ : CommRing R✝\nR : Type u_1\nA : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nS : Submonoid R\ninst✝ : IsLocalization S A\nI : (FractionalIdeal S A)ˣ\nv : A\nhv : v ∈ ↑I⁻¹\nh : Submodule.comap (Algebra.linearMap R A) (↑↑I * Submodule.span ... | [
108,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.card_filter_mem_Icc_le | [
{
"state_after": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx✝ : ι → ℝ\ninst✝ : Fintype ι\nx : ι → ℝ\n⊢ card (filter (fun J => x ∈ ↑Box.Icc J) π.boxes) ≤ Fintype.card (Set ι)",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx✝ : ι → ℝ\ninst✝ : Fintype ι\nx : ι →... | [
207,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_self | [
{
"state_after": "case h0\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\nhs' : Set.Nonempty s\n⊢ ↑↑Measure.count s ≠ 0\n\ncase ht\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\nhs'... | [
109,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_sinh_ofReal_re | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℂ\nx : ℝ\n⊢ ↑(starRingEnd ℂ) (sinh ↑x) = sinh ↑x",
"tactic": "rw [← sinh_conj, conj_ofReal]"
}
] | [
652,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Data/Sign.lean | sign_sum | [
{
"state_after": "case zero\nα : Type u_2\ninst✝ : LinearOrderedAddCommGroup α\nι : Type u_1\ns : Finset ι\nf : ι → α\nhs : Finset.Nonempty s\nh : ∀ (i : ι), i ∈ s → ↑sign (f i) = zero\n⊢ ↑sign (∑ i in s, f i) = zero\n\ncase neg\nα : Type u_2\ninst✝ : LinearOrderedAddCommGroup α\nι : Type u_1\ns : Finset ι\nf :... | [
478,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.lcm_dvd_mul | [] | [
97,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_apply | [
{
"state_after": "no goals",
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903,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero | [
{
"state_after": "Ω : Type u_1\ninst✝ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\nnonzero : μ ≠ 0\n⊢ ProbabilityMeasure.toFiniteMeasure (normalize μ) =\n (mass μ)⁻¹ • mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)",
"state_before": "Ω : Type u_1\ninst✝ : Nonempty Ω\nm0 : Measura... | [
366,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_sup | [] | [
1265,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_singleton_eq_empty | [
{
"state_after": "no goals",
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"tactic": "rw [inter_comm, singleton_inter_eq_empty]"
}
] | [
1351,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1350,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.measurableSet_preimage | [] | [
210,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_single_ne_zero | [
{
"state_after": "case a\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ni : ι\nb : β i\nhb : b ≠ 0\nj : ι\n⊢ j ∈ support (single i b) ↔ j ∈ {i}",
"state_before": "ι : Type u\nγ ... | [
1165,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_inter_lt_top_of_right_ne_top | [] | [
340,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Topology/GDelta.lean | Set.Finite.isGδ | [] | [
170,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/Convex/Between.lean | Function.Injective.wbtw_map_iff | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type u_4\nP : Type u_3\nP' : Type u_5\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\nf : P →ᵃ[R] P'\nhf : Injective ↑f\nh : Wbtw ... | [
164,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_sub_one_eq | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.2780127\nN : Type ?u.2780130\nG : Type ?u.2780133\nR : Type u_1\nS : Type ?u.2780139\nF : Type ?u.2780142\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh : IsPrimitiveRoot ζ✝ k\ni... | [
675,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.map_comp | [
{
"state_after": "case h.mk\nα : Type ?u.31962\nX : Type u_3\nY : Type u_1\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS : DiscreteQuotient X\nf : C(X, Y)\nA A' : DiscreteQuotient X\nB B' : DiscreteQuotient Y\ng : C(Y, Z)\nC : DiscreteQuotient Z\nh1 : LEC... | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.tendsto_fst | [] | [
140,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/List/Sigma.lean | List.keys_kreplace | [
{
"state_after": "case mk.mk\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\na₁ : α\nb₂✝ : β a₁\na₂ : α\nb₂ : β a₂\n⊢ ({ fst := a₂, snd := b₂ } ∈ if a = { fst := a₁, snd := b₂✝ }.fst then some { fst := a, snd := b } else none) →\n { fst := a₁, snd := b₂✝ }.fst = ... | [
374,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_pi | [
{
"state_after": "⊢ ↑(-1) = -1",
"state_before": "⊢ cos ↑π = -1",
"tactic": "rw [← ofReal_cos, Real.cos_pi]"
},
{
"state_after": "no goals",
"state_before": "⊢ ↑(-1) = -1",
"tactic": "simp"
}
] | [
1126,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.denominators_stable_of_terminated | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn m : ℕ\ninst✝ : DivisionRing K\nn_le_m : n ≤ m\nterminated_at_n : TerminatedAt g n\n⊢ denominators g m = denominators g n",
"tactic": "simp only [denom_eq_conts_b, continuants_stable_of_terminated n_le_m ter... | [
85,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_strictMono | [] | [
481,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_sSup | [
{
"state_after": "case h\nι : Sort ?u.90110\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ns : Set (Subgraph G)\nv x✝ : V\n⊢ x✝ ∈ neighborSet (sSup s) v ↔ x✝ ∈ ⋃ (G' : Subgraph G) (_ : G' ∈ s), neighborSet G' v",
"state_before": "ι : Sort ?u.90110\nV : Type u\nW : Type v\nG : Simpl... | [
518,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.cons_left | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : DecidableEq α\nl₁ l₂ : List α\nh✝ : l₁ <+~ l₂\nh : ∀ (x : α), x ∈ l₁ → count x l₁ ≤ count x l₂\nx : α\nhx : count x l₁ < count x l₂\n⊢ ∀ (x_1 : α), x_1 ∈ x :: l₁ → count x_1 (x :: l₁) ≤ count x_1 l₂",
"state_before": "α : Type uu\nβ : Typ... | [
945,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_sub_Ico_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ c✝ d a b c : α\n⊢ Ico a b - Ico a c = Ico (max a c) b",
"tactic": "rw [Ico, Ico, Ico, ← Finset.sdiff_val, Finset.Ico_diff_Ico_left]"
}
] | [
275,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_finset_sup | [
{
"state_after": "R : Type ?u.1100644\nR' : Type ?u.1100647\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1100653\n𝕜₃ : Type ?u.1100656\n𝕝 : Type ?u.1100659\nE : Type u_2\nE₂ : Type ?u.1100665\nE₃ : Type ?u.1100668\nF : Type ?u.1100671\nG : Type ?u.1100674\nι : Type u_3\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCommGroup E\ni... | [
879,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.domCongr_refl | [] | [
1755,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1753,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map.of | [] | [
827,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.contSupp_halt | [] | [
1891,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1890,
1
] |
Mathlib/Data/Set/Image.lean | Set.ball_image_of_ball | [] | [
235,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.inter_right | [] | [
215,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_powerset | [
{
"state_after": "no goals",
"state_before": "x y : ZFSet\nx✝¹ x✝ : PSet\nα : Type u\nA : α → PSet\nβ : Type u\nB : β → PSet\n⊢ PSet.mk β B ∈ PSet.powerset (PSet.mk α A) ↔ Quotient.mk setoid (PSet.mk β B) ⊆ Quotient.mk setoid (PSet.mk α A)",
"tactic": "simp [mem_powerset, subset_iff]"
}
] | [
1013,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.linearProjOfIsCompl_apply_right | [] | [
185,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_injective | [] | [
207,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.mOfFn_pure | [
{
"state_after": "n✝ : ℕ\nα✝ : Type ?u.39247\nm : Type u_1 → Type u_2\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nα : Type u_1\nn : ℕ\nf : Fin (n + 1) → α\n⊢ (do\n let a ← pure (f 0)\n let v ← pure (ofFn fun i => f (Fin.succ i))\n pure (a ::ᵥ v)) =\n pure (f 0 ::ᵥ ofFn fun i => f (Fin.succ i))",... | [
413,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.copy_eq | [] | [
383,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Finset.sum_smul_sum_eq_sum_perm | [
{
"state_after": "ι : Type u_1\nα : Type u_3\nβ : Type u_2\ninst✝³ : DecidableEq α\ninst✝² : Semiring α\ninst✝¹ : AddCommMonoid β\ninst✝ : Module α β\ns : Finset ι\nσ : Perm ι\nhσ : IsCycleOn σ ↑s\nf : ι → α\ng : ι → β\n⊢ ∑ x in range (card s),\n ∑ x_1 in s,\n f\n (↑{ toFun := fun i => (i... | [
1978,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1975,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.fixed_point_card_lt_of_ne_one | [
{
"state_after": "ι : Type ?u.3061128\nα : Type u_1\nβ : Type ?u.3061134\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nσ✝ τ : Perm α\ninst✝ : Fintype α\nσ : Perm α\nh : σ ≠ 1\n⊢ 1 < card (filter (fun x => ¬↑σ x = x) univ)",
"state_before": "ι : Type ?u.3061128\nα : Type u_1\nβ : Type ?u.3061134\ninst✝² : Dec... | [
1828,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1825,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finset_card_le_finrank_of_linearIndependent | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\nb : Finset V\nh : LinearIndependent K fun x => ↑x\n⊢ Fintype.card { x // x ∈ b } ≤ finrank K V",
"stat... | [
292,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagram_r | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.deleteMin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nle : α → α → Bool\na : α\ns' s : Heap α\nh : WF le s\neq : Heap.deleteMin le s = some (a, s')\n⊢ WF le s'",
"tactic": "cases h with cases eq | node h => exact Heap.WF.combine h"
},
{
"state_after": "no goals",
"state_before": "case ... | [
255,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
253,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.of_right_adjoint | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : IsFiltered C\nO : Finset C\nH : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))\nJ : Type v\ninst✝² : SmallCategory J\ninst✝¹ : FinCategory J\nD : Type u₁\ninst✝ : Category D\nL : D ⥤ C\nR : C ⥤ D\nh... | [
319,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.tanh_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ tanh 0 = 0",
"tactic": "simp [tanh]"
}
] | [
1395,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
1
] |
Mathlib/CategoryTheory/Category/Grpd.lean | CategoryTheory.Grpd.coe_of | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_span_mul_finite_of_mem_mul | [
{
"state_after": "no goals",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P✝ Q✝ : Submodule R A\nm n : A\nP Q : Submodule R A\nx : A\nhx : x ∈ P * Q\n⊢ x ∈ span R (↑P * ↑Q)",
"tactic": "rwa [← Submodule.span_eq ... | [
368,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/ContinuousOn.lean | map_nhdsWithin | [] | [
363,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sinh (x - y) = sinh x * cosh y - cosh x * sinh y",
"tactic": "simp [sub_eq_add_neg, sinh_add, sinh_neg, cosh_neg]"
}
] | [
1383,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1382,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasLimit_of_hasColimit_leftOp | [] | [
245,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.lift.tprod | [] | [
419,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_prod_val | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Encodable α\ninst✝ : Encodable β\ni : Encodable α\nn : ℕ\n⊢ Option.map (↑(Equiv.sigmaEquivProd α β))\n (Option.bind (decode (unpair n).fst) fun a => Option.map (Sigma.mk a) (decode (unpair n).snd)) =\n Option.bind (decode (unpair n).fst) fun a => Op... | [
393,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_normalizer_of_normal | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.385870\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.385879\ninst✝ : AddGroup A\nH K : Subgroup G\nhK : Normal (subgroupOf H K)\nHK : H ≤ K\nx : G\nhx : x ∈ K\ny : G\nyH : x * y * x⁻¹ ∈ H\n⊢ y ∈ H",
"tactic": "simpa [mem_subgro... | [
2204,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2200,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.pow_coeff | [] | [
386,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
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