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/Subgroup/Basic.lean | MonoidHom.closure_preimage_le | [
{
"state_after": "G : Type u_1\nG' : Type ?u.550439\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.550448\ninst✝² : AddGroup A\nN : Type u_2\nP : Type ?u.550457\ninst✝¹ : Group N\ninst✝ : Group P\nK : Subgroup G\nf : G →* N\ns : Set N\nx : G\nhx : x ∈ ↑f ⁻¹' s\n⊢ ↑f x ∈ closure s",
"state_before": "G : T... | [
2926,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2925,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_ne_empty | [] | [
142,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.compl_erase | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.11642\nγ : Type ?u.11645\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : DecidableEq α\na a✝ : α\n⊢ a✝ ∈ erase s aᶜ ↔ a✝ ∈ insert a (sᶜ)",
"state_before": "α : Type u_1\nβ : Type ?u.11642\nγ : Type ?u.11645\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : Decidab... | [
224,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.union_apply_right | [] | [
247,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_eq_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nP : α → Prop\nm : (s : α) → P s → ℝ≥0∞\ns : α\nh : ¬P s\n⊢ extend m s = ⊤",
"tactic": "simp [extend, h]"
}
] | [
1325,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_clm_comp | [] | [
113,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_add_le_of_le_add | [
{
"state_after": "a b c : Int\nh✝ : a ≤ b + c\nh : -b + a ≤ -b + (b + c)\n⊢ -b + a ≤ c",
"state_before": "a b c : Int\nh : a ≤ b + c\n⊢ -b + a ≤ c",
"tactic": "have h := Int.add_le_add_left h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a ≤ b + c\nh : -b + a ≤ -b ... | [
980,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
978,
11
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_one | [] | [
380,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toAdd_div | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_apply_bot | [] | [
934,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/Topology/Category/Profinite/Basic.lean | Profinite.epi_iff_surjective | [
{
"state_after": "case mp\nX✝ Y✝ : Profinite\nf✝ : X✝ ⟶ Y✝\nX Y : Profinite\nf : X ⟶ Y\n⊢ Epi f → Function.Surjective ((forget Profinite).map f)\n\ncase mpr\nX✝ Y✝ : Profinite\nf✝ : X✝ ⟶ Y✝\nX Y : Profinite\nf : X ⟶ Y\n⊢ Function.Surjective ((forget Profinite).map f) → Epi f",
"state_before": "X✝ Y✝ : Profi... | [
413,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.modify_size | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β → β\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nk : α\nh : m.size = Bucket.size m.buckets\n⊢ m.size =\n Bucket.size\n (Bucket.update\n (Bucket.update m.buckets (mkIdx (_ : 0 < Array.size m.buckets.val) (UInt64.toUSize (hash k))).val As... | [
271,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
265,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_le_inter_le | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\na : α\n⊢ Bounded (fun x x_1 => x ≤ x_1) (s ∩ {b | a ≤ b}) → Bounded (fun x x_1 => x ≤ x_1) s",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\na : α\n⊢ Bounded (fun x x_1 => x ≤ x_1) (s... | [
345,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_prod | [] | [
2009,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2006,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_zero_lf | [
{
"state_after": "x : PGame\n⊢ ((∀ (i : LeftMoves x), moveLeft x i ⧏ 0) ∧ ∀ (j : RightMoves 0), x ⧏ moveRight 0 j) ↔\n ∀ (i : LeftMoves x), moveLeft x i ⧏ 0",
"state_before": "x : PGame\n⊢ x ≤ 0 ↔ ∀ (i : LeftMoves x), moveLeft x i ⧏ 0",
"tactic": "rw [le_iff_forall_lf]"
},
{
"state_after": "n... | [
651,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Order/BoundedOrder.lean | monotone_lt | [] | [
568,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.hasBasis_nhds | [] | [
694,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
11
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv_self | [] | [
775,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Algebra/Support.lean | Pi.mulSupport_mulSingle_subset | [] | [
467,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnity.coe_pow | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.368159\nN : Type ?u.368162\nG : Type ?u.368165\nR : Type u_1\nS : Type ?u.368171\nF : Type ?u.368174\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ninst✝¹ : DivisionCommMonoid G\nk l : ℕ+\ninst✝ : CommMonoid R\nζ : { x // x ∈ rootsOfUnity k R }\nm : ... | [
136,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_cons_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na b : α\nh : R b a\n⊢ destutter' R b (a :: l) = b :: destutter' R a l",
"tactic": "rw [destutter', if_pos h]"
}
] | [
52,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_eq_foldr | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12132\nα : Type ?u.12135\nM : Type u_1\nN : Type ?u.12141\nP : Type ?u.12144\nM₀ : Type ?u.12147\nG : Type ?u.12150\nR : Type ?u.12153\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl✝ l₁ l₂ : List M\na✝ a : M\nl : List M\n⊢ prod (a :: l) =... | [
75,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Ioc | [] | [
151,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
11
] |
Mathlib/Data/Set/NAry.lean | Set.image_image2_antidistrib_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nα' : Type ?u.47893\nβ : Type u_4\nβ' : Type u_5\nγ : Type u_2\nγ' : Type ?u.47905\nδ : Type u_1\nδ' : Type ?u.47911\nε : Type ?u.47914\nε' : Type ?u.47917\nζ : Type ?u.47920\nζ' : Type ?u.47923\nν : Type ?u.47926\nf f'✝ : α → β → γ\ng✝ g'✝ : α → β ... | [
408,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.eq_iff | [
{
"state_after": "case mp\nG : Type u_1\nG' : Type ?u.513580\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.513589\ninst✝³ : AddGroup A\nN : Type ?u.513595\nP : Type ?u.513598\ninst✝² : Group N\ninst✝¹ : Group P\nK : Subgroup G\nM : Type u_2\ninst✝ : MulOneClass M\nf : G →* M\nx y : G\nh : ↑f x = ↑f y\n⊢ y⁻¹... | [
2788,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2785,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.lift_extend | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ F : J ⥤ C\ninst✝ : HasLimit F\nc : Cone F\nX : C\nf : X ⟶ c.pt\n⊢ lift F (Cone.extend c f) = f ≫ lift F c",
"tactic": "aesop_cat"
}
] | [
312,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.Tendsto.mul_mul | [] | [
635,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.image_eq_image | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝³ : Category V\ninst✝² : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝¹ : HasImages V\ninst✝ : HasEqualizers V\ni i' j : ι\nr : ComplexShape.Rel c i j\nr' : ComplexShape.Rel c i' j\n⊢ imageSubobject (eqToHom (_ : X C i = X C i') ≫ d C ... | [
344,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.isPathConnected | [
{
"state_after": "ι : Type ?u.191359\n𝕜 : Type ?u.191362\nE : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\ns : Set E\nhconv : Convex ℝ s\nhne : Set.Nonempty s\n⊢ ∀ (x : E), x ∈ s → ∀ (y : E), y ∈ s → JoinedIn s ... | [
350,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
11
] |
Mathlib/RingTheory/IntegralClosure.lean | FG_adjoin_of_finite | [
{
"state_after": "R : Type u_2\nA : Type u_1\nB : Type ?u.318888\nS : Type ?u.318891\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\ns : Set A\nhfs : Set.Finite s\nhis : ∀ (x : A), x ∈ s → IsIntegral R x\nx✝ : ∀ (x : A)... | [
244,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/Matrix/Basic.lean | AddMonoidHom.mapMatrix_id | [] | [
1413,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1412,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.sigmaComparison_map_desc | [
{
"state_after": "case h\nβ : Type w\nC : Type u\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nG : C ⥤ D\nf : β → C\ninst✝¹ : HasCoproduct f\ninst✝ : HasCoproduct fun b => G.obj (f b)\nP : C\ng : (j : β) → f j ⟶ P\nj : β\n⊢ Sigma.ι (fun b => G.obj (f b)) j ≫ sigmaComparison G f ≫ G.map (Sigma.desc g) ... | [
279,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integrable_prod_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.2396048\nβ : Type u_2\nβ' : Type ?u.2396054\nγ : Type ?u.2396057\nE : Type u_3\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : Measur... | [
280,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Std/Data/List/Init/Lemmas.lean | List.mapM'_eq_mapM | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → m β\nl : List α\n⊢ mapM' f l = mapM f l",
"tactic": "simp [go, mapM]"
},
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\n... | [
216,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
212,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sup_eq_max | [] | [
743,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
9
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_eq_bot | [] | [
255,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_eq_preimage' | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.77374\nι : Sort ?u.77377\nι' : Sort ?u.77380\nf✝ : ι → α\ns✝ t✝ s t : Set α\nf : β → α\nhs : s ⊆ range f\nht : t ⊆ range f\n⊢ f ⁻¹' s = f ⁻¹' t → s = t\n\ncase mpr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.77374\nι : Sort ?u.77377\nι' : Sort ?u.7... | [
836,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.exists_minimal_degree_vertex | [
{
"state_after": "case intro\nι : Sort ?u.289282\n𝕜 : Type ?u.289285\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✝² : Fintype V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Nonempty V\nt : ℕ\nht : Finset.min (image (fun v => degree G v) univ) = ↑t\n⊢ ∃ ... | [
1518,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/GroupTheory/Solvable.lean | not_solvable_of_mem_derivedSeries | [] | [
213,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.X_mul_divMonomial | [] | [
166,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.add_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.11263\nδ : Type ?u.11266\na : α\ns t : Multiset α\nf g : α → Multiset β\n⊢ bind (s + t) f = bind s f + bind t f",
"tactic": "simp [bind]"
}
] | [
119,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ne_of_mem_erase | [] | [
1879,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1879,
1
] |
Mathlib/Order/Heyting/Basic.lean | hnot_anti | [] | [
1083,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.hasColimits_of_reflective | [] | [
390,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.eval_one | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : Field K\nL : Type u_1\ninst✝ : Field L\nf : K →+* L\na : L\n⊢ eval f a 1 = 1",
"tactic": "simp [eval]"
}
] | [
1503,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1503,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.prod_same_index_anti | [] | [
932,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.div_closedBall | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx✝ y : E\nhs : IsCompact s\nhδ : 0 ≤ δ\nx : E\n⊢ s / closedBall x δ = x⁻¹ • cthickening δ s",
"tactic": "simp [div_eq_mul_inv, mul_comm, hs.mul_closedBall hδ]"
}
] | [
293,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_zero | [] | [
62,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_C | [] | [
55,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.forall_mem_map_iff | [] | [
1162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.eq | [] | [
73,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
11
] |
Mathlib/Algebra/AddTorsor.lean | Equiv.pointReflection_fixed_iff_of_injective_bit0 | [
{
"state_after": "no goals",
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"tactic": "rw [pointReflection_apply, eq_comm, eq_vadd_iff_vsub_eq, ← neg_vsub_eq_vsub_rev,\n neg_eq_iff_add_eq_zero,... | [
471,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.pentagon | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nW : ModuleCat R\nX : ModuleCat R\nY : ModuleCat R\nZ : ModuleCat R\n⊢ tensorHom (associator W X Y).hom (𝟙 Z) ≫\n (associator W (tensorObj X Y) Z).hom ≫ tensorHom (𝟙 W) (associator X Y Z).hom =\n (associator (tensorObj W ... | [
135,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.coe_ereal_ennreal | [] | [
2018,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2016,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | jacobi_cross | [] | [
166,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.mem_support_iff | [] | [
97,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | norm_add_lt_of_not_sameRay | [
{
"state_after": "𝕜 : Type ?u.54272\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : StrictConvexSpace ℝ E\nx y z : E\na b r : ℝ\nh : x ≠ 0 ∧ y ≠ 0 ∧ ‖x‖⁻¹ • x ≠ ‖y‖⁻¹ • y\n⊢ ‖x + y‖ < ‖x‖ + ‖y‖",
"state_before"... | [
194,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.commute_sub_int | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℤ\n⊢ Function.Commute ↑f fun x => x - ↑n",
"tactic": "simpa only [sub_eq_add_neg] using\n (f.commute_add_int n).inverses_right (Equiv.addRight _).right_inv (Equiv.addRight _).left_inv"
}
] | [
358,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_prime_pow_eq_geom_sum | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\np n : ℕ\nhp : Nat.Prime p\nthis :\n ∀ (m : ℕ),\n cyclotomic (p ^ (m + 1)) R = ∑ i in range p, (X ^ p ^ m) ^ i ↔\n (∑ i in range p, (X ^ p ^ m) ^ i) * ∏ x in range (m + 1), cyclotomic (p ^ x) R = X ^ p ^ (m + 1) - 1\n⊢ cyclotomic (p ^ (n + 1)) R = ∑ i ... | [
576,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_congr | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.68613\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\nh : Set.EqOn f g ↑s\na✝ : β\n⊢ a✝ ∈ image f s ↔ a✝ ∈ image g s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.68613\ninst✝ : DecidableEq β\nf g... | [
361,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toHomeomorph_inj | [] | [
668,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/Set/Image.lean | Set.exists_subset_range_iff | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
813,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_inv_of_pos | [
{
"state_after": "no goals",
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"tactic": "rw [ENNReal.ofReal, ENNReal.ofReal, ← @coe_inv (Real.toNNReal x) (by simp [hx]), coe_eq_coe,\n ← Real.toNNReal_i... | [
2187,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2185,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | WfDvdMonoid.exists_irreducible_factor | [] | [
93,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMonoOn.monotoneOn | [] | [
458,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.zero_eq_ofReal | [] | [
2123,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2122,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.coe_copy | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Separation.lean | separated_by_openEmbedding | [] | [
1131,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Mathlib/Data/Sum/Interval.lean | Sum.Ico_inl_inr | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_add_eq_iff_add_mul_eq_mul | [
{
"state_after": "no goals",
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296,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Set/Image.lean | Set.subset_image_symm_diff | [] | [
438,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_conjTranspose | [] | [
75,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.leftDual_ρ | [
{
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754,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_ofDual | [] | [
2315,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2314,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.range_coe_eq_Ioo | [
{
"state_after": "case h\nx : EReal\n⊢ x ∈ range Real.toEReal ↔ x ∈ Ioo ⊥ ⊤",
"state_before": "⊢ range Real.toEReal = Ioo ⊥ ⊤",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case h\nx : EReal\n⊢ x ∈ range Real.toEReal ↔ x ∈ Ioo ⊥ ⊤",
"tactic": "induction x using ERea... | [
351,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.coe_tsub | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.le_ceil | [] | [
1126,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/Algebra/GroupWithZero/Power.lean | div_sq_cancel | [
{
"state_after": "case pos\nG₀ : Type u_1\ninst✝ : CommGroupWithZero G₀\na b : G₀\nha : a = 0\n⊢ a ^ 2 * b / a = a * b\n\ncase neg\nG₀ : Type u_1\ninst✝ : CommGroupWithZero G₀\na b : G₀\nha : ¬a = 0\n⊢ a ^ 2 * b / a = a * b",
"state_before": "G₀ : Type u_1\ninst✝ : CommGroupWithZero G₀\na b : G₀\n⊢ a ^ 2 * ... | [
198,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_eq_one_iff_inv_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.53359\nβ : Type ?u.53362\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ a * b = 1 ↔ a⁻¹ = b",
"tactic": "rw [mul_eq_one_iff_eq_inv, inv_eq_iff_eq_inv]"
}
] | [
675,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.pair_apply | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/Basic.lean | isOpen_singleton_iff_nhds_eq_pure | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\na : α\n⊢ IsOpen {a} → 𝓝 a = pure a\n\ncase mpr\nα : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\na : α\n⊢ 𝓝 a ... | [
1257,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasStrictFDerivAt | [] | [
633,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Logic/Hydra.lean | Relation.cutExpand_fibration | [
{
"state_after": "case mk.intro.intro.intro\nα : Type u_1\nr✝ r : α → α → Prop\ns₁ s₂ s t : Multiset α\na : α\nhr : ∀ (a' : α), a' ∈ t → r a' a\nhe : s + {a} = (fun s => s.fst + s.snd) (s₁, s₂) + t\n⊢ ∃ a', GameAdd (CutExpand r) (CutExpand r) a' (s₁, s₂) ∧ (fun s => s.fst + s.snd) a' = s",
"state_before": "... | [
127,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_one | [] | [
137,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_sub | [] | [
673,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.sum_mul_boole | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nb : β\nf✝ g : α → β\ninst✝¹ : NonAssocSemiring β\ninst✝ : DecidableEq α\ns : Finset α\nf : α → β\na : α\n⊢ (∑ x in s, f x * if a = x then 1 else 0) = if a ∈ s then f a else 0",
"tactic": "simp"... | [
77,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.ofEquiv_card | [] | [
149,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Computability/Ackermann.lean | ack_le_iff_right | [] | [
165,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.sup_adj | [] | [
255,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_zero | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/GroupTheory/Commutator.lean | Commute.commutator_eq | [] | [
41,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | List.stronglyMeasurable_prod' | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.109795\nγ : Type ?u.109798\nι : Type ?u.109801\ninst✝³ : Countable ι\nf g : α → β\nM : Type u_2\ninst✝² : Monoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : ContinuousMul M\nm : MeasurableSpace α\nl : List (α → M)\nhl✝ : ∀ (f : α → M), f ∈ l → StronglyMeasurable... | [
548,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.of_mul_right | [] | [
393,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.supported_mono | [] | [
116,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.Iic_eq_powerset | [] | [
69,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.mem_interedges_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.1103\nι : Type ?u.1106\nκ : Type ?u.1109\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nx : α × β\n⊢ x ∈ interedges ... | [
61,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.im_le_abs | [] | [
1047,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.emod_two_eq_zero_or_one | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nn✝ : ℕ\nn : ℤ\n⊢ 0 ≤ 2",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "a b : ℤ\nn✝ : ℕ\nn : ℤ\n⊢ abs 2 ≠ 0",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "a b : ℤ\nn✝ : ℕ\nn : ℤ... | [
330,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Set/Image.lean | Set.mem_preimage | [] | [
68,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.right_le_of_le_left'' | [] | [
1107,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
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