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/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.toLin'_symm_apply | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.id_map | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nx : F α\n⊢ id <$> abs (repr x) = abs (repr x)",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nx : F α\n⊢ id <$> x = x",
"tactic": "rw [← abs_repr x]"
},
{
"state_after": "case mk\nF... | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_zsmul | [] | [
759,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_injective_iff | [
{
"state_after": "case refine'_1\nm n : ℕ\nα✝ : Fin (n + 1) → Type u\nx✝ : α✝ 0\nq : (i : Fin (n + 1)) → α✝ i\np : (i : Fin n) → α✝ (succ i)\ni : Fin n\ny : α✝ (succ i)\nz : α✝ 0\nα : Type u_1\nx₀ : α\nx : Fin n → α\nh : Injective (cons x₀ x)\n⊢ ¬x₀ ∈ Set.range x\n\ncase refine'_2\nm n : ℕ\nα✝ : Fin (n + 1) → T... | [
196,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.isClosed_image_polar_of_mem_nhds | [] | [
234,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.self_trans_symm | [] | [
574,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | inf_mul | [] | [
94,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean | Matrix.eq_zero_of_vecMul_eq_zero | [
{
"state_after": "no goals",
"state_before": "m : Type u_1\nR : Type ?u.16431\nA : Type u_2\ninst✝⁴ : Fintype m\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : IsDomain A\ninst✝ : DecidableEq m\nM : Matrix m m A\nhM : det M ≠ 0\nv : m → A\nhv : vecMul v M = 0\nw : m → A\n⊢ v ⬝ᵥ mulVec M w = 0",
"tac... | [
72,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_closure_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\ns : Set R\n⊢ ↑(closure s) = ↑(AddSubmonoid.closure ↑(Submonoid.closure s))",
"tactic": "simp [← Submonoid.subsemiringCl... | [
896,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableAt.continuousAt | [] | [
739,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.coinduced_of_isColimit | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TopCatMax\nc : Cocone F\nhc : IsColimit c\nhomeo : ↑c.pt ≃ₜ ↑(colimitCocone F).pt := homeoOfIso (IsColimit.coconePointUniqueUpToIso hc (colimitCoconeIsColimit F))\n⊢ c.pt.str = ⨆ (j : J), coinduced ((forget TopCat).map (c.ι.app j)) (F.obj j).str",
... | [
406,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | exists_pow_eq_self_of_coprime | [
{
"state_after": "case pos\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nh : coprime n (orderOf x)\nh0 : orderOf x = 0\n⊢ ∃ m, (x ^ n) ^ m = x\n\ncase neg\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nh : coprime n (orde... | [
296,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/List/Zip.lean | List.length_revzip | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.93218\nγ : Type ?u.93221\nδ : Type ?u.93224\nε : Type ?u.93227\nl : List α\n⊢ length (revzip l) = length l",
"tactic": "simp only [revzip, length_zip, length_reverse, min_self]"
}
] | [
344,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.comp_assoc | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mrange_top_of_surjective | [] | [
1078,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists_eq_sublists' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ sublists l = map reverse (sublists' (reverse l))",
"tactic": "rw [← sublists_reverse, reverse_reverse]"
}
] | [
190,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.nhds_σ | [] | [
228,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.pow_card_pow | [
{
"state_after": "case zero\nK : Type ?u.1002572\nR : Type ?u.1002575\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : ZMod p\n⊢ x ^ p ^ Nat.zero = x\n\ncase succ\nK : Type ?u.1002572\nR : Type ?u.1002575\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : ZMod p\nn : ℕ\nih : x ^ p ^ n = x\n⊢ x ^ p ^ Nat.succ n = x",
"state_bef... | [
413,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Algebra/Order/Hom/Basic.lean | map_pos_of_ne_one | [] | [
311,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FinitePresentation.comp | [] | [
511,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_mono_right | [
{
"state_after": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr₁ r₂ : R\nh₀ : 0 < r₁\nh : r₁ ≤ r₂\n⊢ log b r₂⁻¹ ≤ log b r₁⁻¹",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr₁ r₂ : R\nh₀ : 0 < r₁\nh : r₁ ≤ r₂\n⊢ clog b ... | [
279,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_prod_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.5367515\nβ : Type u_2\nβ' : Type ?u.5367521\nγ : Type ?u.5367524\nE : Type ?u.5367527\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' :... | [
804,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ioc_coe_coe | [] | [
1176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.eq_enumOrd | [
{
"state_after": "case mp\nS : Set Ordinal\nf : Ordinal → Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\n⊢ StrictMono f ∧ range f = S → f = enumOrd S\n\ncase mpr\nS : Set Ordinal\nf : Ordinal → Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\n⊢ f = enumOrd S → StrictMono f ∧ range f = S",
"state_before"... | [
2284,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2278,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_append_eq_append_drop | [
{
"state_after": "case nil\nι : Type ?u.204814\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nn : ℕ\n⊢ drop n ([] ++ l₂) = drop n [] ++ drop (n - length []) l₂\n\ncase cons\nι : Type ?u.204814\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nhead✝ : α\ntail✝ : List α\nt... | [
2178,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2175,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_mul_cancel | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a⁻¹ * b * a = b",
"tactic": "rw [h.inv_left.eq, inv_mul_cancel_right]"
}
] | [
380,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
11
] |
Mathlib/NumberTheory/LucasLehmer.lean | one_lt_mersenne | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : 1 < p\n⊢ 1 + 1 = 2 ^ 1",
"tactic": "rw [one_add_one_eq_two, pow_one]"
}
] | [
59,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_nat_pow_near_of_lt_one | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\nx y ε : α\nxpos : 0 < x\nhx : x ≤ 1\nypos : 0 < y\nhy : y < 1\nn : ℕ\nhn : y⁻¹ ^ n ≤ x⁻¹\nh'n : x⁻¹ < y⁻¹ ^ (n + 1)\n⊢ ∃ n, y ^ (n + 1) < x ∧ x ≤ y ^ n",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrde... | [
250,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Nat/Pairing.lean | Set.iUnion_unpair_prod | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ns : ℕ → Set α\nt : ℕ → Set β\n⊢ (⋃ (n : ℕ), s (unpair n).fst ×ˢ t (unpair n).snd) = ⋃ (x : ℕ × ℕ), s x.fst ×ˢ t x.snd",
"state_before": "α : Type u_1\nβ : Type u_2\ns : ℕ → Set α\nt : ℕ → Set β\n⊢ (⋃ (n : ℕ), s (unpair n).fst ×ˢ t (unpair n).snd) = (⋃ (n : ℕ), s... | [
209,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/RingTheory/Artinian.lean | isArtinian_span_of_finite | [] | [
368,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_zero | [
{
"state_after": "x : PGame\n⊢ ((∀ (i : LeftMoves x), (∃ i', moveLeft x i ≤ moveLeft 0 i') ∨ ∃ j, moveRight (moveLeft x i) j ≤ 0) ∧\n ∀ (j : RightMoves 0), (∃ i, x ≤ moveLeft (moveRight 0 j) i) ∨ ∃ j', moveRight x j' ≤ moveRight 0 j) ↔\n ∀ (i : LeftMoves x), ∃ j, moveRight (moveLeft x i) j ≤ 0",
"st... | [
675,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_right_identity | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.45411\nβ : Type u_2\nβ' : Type ?u.45417\nγ : Type ?u.45420\nγ' : Type ?u.45423\nδ : Type ?u.45426\nδ' : Type ?u.45429\nε : Type ?u.45432\nε' : Type ?u.45435\nm : α → β → γ\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh✝ h₁ h₂ : Filter γ\n... | [
420,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.get_last | [
{
"state_after": "case mk\nα : Type u_1\na : α\nas : List α\nval✝ : Nat\nisLt✝ : val✝ < length (as ++ [a])\nh : ¬{ val := val✝, isLt := isLt✝ }.val < length as\n⊢ get (as ++ [a]) { val := val✝, isLt := isLt✝ } = a",
"state_before": "α : Type u_1\na : α\nas : List α\ni : Fin (length (as ++ [a]))\nh : ¬i.val ... | [
117,
41
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
109,
1
] |
Mathlib/Topology/Maps.lean | IsClosedMap.comp | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.198255\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ng : β → γ\nf : α → β\nhg : IsClosedMap g\nhf : IsClosedMap f\ns : Set α\nhs : IsClosed s\n⊢ IsClosed (g ∘ f '' s)",
"state_before": "α : Type ... | [
490,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
11
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_le_iff_mem | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₂ : Type ?u.222780\nK : Type ?u.222783\nM : Type u_2\nM₂ : Type ?u.222789\nV : Type ?u.222792\nS : Type ?u.222795\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np✝ p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* ... | [
654,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
src/lean/Init/Meta.lean | Lean.Name.beq_iff_eq | [
{
"state_after": "sep : String\nescape : Bool\nm n : Name\n⊢ Name.beq m n = true ↔ m = n",
"state_before": "sep : String\nescape : Bool\nm n : Name\n⊢ (m == n) = true ↔ m = n",
"tactic": "show m.beq n ↔ _"
},
{
"state_after": "no goals",
"state_before": "sep : String\nescape : Bool\nm n : Na... | [
209,
75
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
207,
11
] |
Mathlib/Order/Grade.lean | grade_top | [] | [
218,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.pair_lt_max_add_one_sq | [
{
"state_after": "m n : ℕ\n⊢ (if m < n then n * n + m else m * m + (m + n)) < max m n * max m n + (max m n + max m n + 1 ^ 2)",
"state_before": "m n : ℕ\n⊢ pair m n < (max m n + 1) ^ 2",
"tactic": "rw [pair, add_sq, mul_one, two_mul, sq, add_assoc, add_assoc]"
},
{
"state_after": "case inl\nm n ... | [
161,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.mk_symm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.15747\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\nZ : Type ?u.15761\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\nproj : Z → B\ne✝ : Pretrivialization F proj\nx : Z\ne' : Pretrivialization F TotalSpace.proj\nx' : TotalSpace E\nb✝ : B\... | [
276,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_apply_eq_div' | [] | [
177,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/CategoryTheory/Limits/Presheaf.lean | CategoryTheory.coconeOfRepresentable_naturality | [
{
"state_after": "case w.h.h\nC : Type u₁\ninst✝¹ : SmallCategory C\nℰ : Type u₂\ninst✝ : Category ℰ\nA : C ⥤ ℰ\nP₁ P₂ : Cᵒᵖ ⥤ Type u₁\nα : P₁ ⟶ P₂\nj : (Functor.Elements P₁)ᵒᵖ\nT : Cᵒᵖ\nf : ((functorToRepresentables P₁).obj j).obj T\n⊢ ((coconeOfRepresentable P₁).ι.app j ≫ α).app T f =\n ((coconeOfRepresent... | [
352,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.shiftr_eq_div_pow | [
{
"state_after": "no goals",
"state_before": "m k : ℕ\n⊢ div2 (m / 2 ^ k) = m / 2 ^ (k + 1)",
"tactic": "rw [div2_val, Nat.div_div_eq_div_mul, Nat.pow_succ]"
}
] | [
54,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.natCast_val | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nR : Type u_3\nA : Type u_1\ninst✝⁵ : AddCommMonoid ι\ninst✝⁴ : DecidableEq ι\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : Submonoid A\nn : ℕ\n⊢ val (Nat.unaryCast n) = ↑n",
... | [
465,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Complex/Exponential.lean | cauchy_product | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\nabv : β → α\ninst✝¹ : Ring β\ninst✝ : IsAbsoluteValue abv\na b : ℕ → β\nha : IsCauSeq abs' fun m => ∑ n in range m, abv (a n)\nhb : IsCauSeq abv fun m => ∑ n in range m, b n\nε : α\nε0 : 0 < ε\nQ : α\nhQ... | [
339,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Nat.cofinite_eq_atTop | [
{
"state_after": "ι : Type ?u.6011\nα : Type ?u.6014\nβ : Type ?u.6017\nl : Filter α\n⊢ cofinite ≤ atTop",
"state_before": "ι : Type ?u.6011\nα : Type ?u.6014\nβ : Type ?u.6017\nl : Filter α\n⊢ cofinite = atTop",
"tactic": "refine' le_antisymm _ atTop_le_cofinite"
},
{
"state_after": "ι : Type ?... | [
150,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.smul_ball | [] | [
277,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.continuousOn_mul | [
{
"state_after": "X : Type u_1\nY : Type ?u.2497686\nE : Type ?u.2497689\nR : Type u_2\ninst✝⁹ : MeasurableSpace X\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : MeasurableSpace Y\ninst✝⁶ : TopologicalSpace Y\ninst✝⁵ : NormedAddCommGroup E\nf✝ : X → E\nμ : Measure X\ns✝ : Set X\ninst✝⁴ : OpensMeasurableSpace X\nA K : S... | [
456,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_append | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.503158\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l✝ : List α\nx : α\nxs : List α\nd✝ : α\nn✝ : ℕ\nl l' : List α\nd : α\nn : ℕ\nh : n < length l\nh' : optParam (n < length (l ++ l')) (_ : n < length (l ++ l'))\n⊢ getD (l ++ l') n d = getD... | [
4430,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4427,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_mem_compression | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a b : α\nha : a ∈ s\n⊢ compress u v a ∈ s ∧ compress u v (compress u v a) ∈ s ∨\n ¬compress u v a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = compress u v... | [
180,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.X_dvd_iff_modMonomial_eq_zero | [] | [
215,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_const | [] | [
1070,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_zero_le | [
{
"state_after": "x : PGame\n⊢ ((∃ i, x ≤ moveLeft 0 i) ∨ ∃ j, moveRight x j ≤ 0) ↔ ∃ j, moveRight x j ≤ 0",
"state_before": "x : PGame\n⊢ x ⧏ 0 ↔ ∃ j, moveRight x j ≤ 0",
"tactic": "rw [lf_iff_exists_le]"
},
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ ((∃ i, x ≤ moveLeft 0 i)... | [
663,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.eq_mk_iff_val_eq | [] | [
219,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousOn_biInf | [] | [
1049,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_add | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_monomial | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nn : ℕ\nr : R\ni : ℕ\n⊢ coeff (↑(hasseDeriv k) (↑(monomial n) r)) i = coeff (↑(monomial (n - k)) (↑(choose n k) * r)) i",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nn : ℕ\nr : R\n⊢ ↑(hasseDeriv k) (↑(monomia... | [
129,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.curry_uncurry | [] | [
208,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_lt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.89670\nγ : Type ?u.89673\nδ : Type ?u.89676\ninst✝ : LT α\na b : α\nx : WithTop α\n⊢ ↑a < x ↔ ∀ (b : WithTop α), x = b → ↑a < b",
"tactic": "simp"
}
] | [
1084,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_range | [] | [
596,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.mono | [] | [
145,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.obj_ε_inv_app | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nn : M\nX : C\n⊢ (F.obj n).map ((MonoidalFunctor.εIso F).inv.app X ≫ F.ε.app X) =\n ((LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor (𝟙_ M) n).app X ≫ (F.map (λ_ n).ho... | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_prod | [] | [
1646,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.pow_apply' | [
{
"state_after": "case pos\nR : Type u\ninst✝¹ : CommMonoid R\nR' : Type v\ninst✝ : CommMonoidWithZero R'\nχ : MulChar R R'\nn : ℕ\nhn : 0 < n\na : R\nha : IsUnit a\n⊢ ↑(χ ^ n) a = ↑χ a ^ n\n\ncase neg\nR : Type u\ninst✝¹ : CommMonoid R\nR' : Type v\ninst✝ : CommMonoidWithZero R'\nχ : MulChar R R'\nn : ℕ\nhn : ... | [
416,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_strictMono_right' | [] | [
176,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_comm | [
{
"state_after": "n m : Nat\nthis : succ (n + m) = succ (m + n)\n⊢ n + (m + 1) = m + 1 + n",
"state_before": "n m : Nat\n⊢ n + (m + 1) = m + 1 + n",
"tactic": "have : succ (n + m) = succ (m + n) := by apply congrArg; apply Nat.add_comm"
},
{
"state_after": "n m : Nat\nthis : succ (n + m) = succ ... | [
136,
15
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
131,
11
] |
Mathlib/Data/Part.lean | Part.union_def | [] | [
706,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.normal_of_all_max_subgroups_normal | [
{
"state_after": "case inl\nG : Type u\nα : Type v\nβ : Type w\ninst✝³ : Group G\ninst✝² : Finite G\nhnc : ∀ (H : Subgroup G), IsCoatom H → Normal H\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Finite (Sylow p G)\nP : Sylow p G\nheq : normalizer ↑P = ⊤\n⊢ normalizer ↑P = ⊤\n\ncase inr.intro.intro\nG : Type u\nα... | [
751,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.exists_irreducible_of_degree_pos | [] | [
971,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_singleton_le_iff_mem | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.21166\nA : Type ?u.21169\ninst✝¹ : Mul M\ns : Set M\ninst✝ : Add A\nt : Set A\nS : Subsemigroup M\nm : M\np : Subsemigroup M\n⊢ closure {m} ≤ p ↔ m ∈ p",
"tactic": "rw [closure_le, singleton_subset_iff, SetLike.mem_coe]"
}
] | [
446,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_inter' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.233733\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
479,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicatorAux_subset | [] | [
123,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.dropSlice_inter | [
{
"state_after": "α✝ : Type uu\nβ : Type vv\nl₁ l₂ : List α✝\nα : Type u_1\ninst✝ : DecidableEq α\nxs ys : List α\nn m : ℕ\nh : xs ~ ys\nh' : Nodup ys\n⊢ take n xs ++ drop (n + m) xs ~ ys ∩ (take n xs ++ drop (n + m) xs)",
"state_before": "α✝ : Type uu\nβ : Type vv\nl₁ l₂ : List α✝\nα : Type u_1\ninst✝ : De... | [
1194,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/Algebra/Invertible.lean | Commute.invOf_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Monoid α\na b : α\ninst✝ : Invertible b\nh : Commute a b\n⊢ a * ⅟b = ⅟b * (b * a * ⅟b)",
"tactic": "simp [mul_assoc]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Monoid α\na b : α\ninst✝ : Invertible... | [
328,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.map_Ici | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.111542\nι : Sort ?u.111545\nκ : ι → Sort ?u.111550\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns : UpperSet α\na✝ b : α\nf : α ≃o β\na : α\nx✝ : β\n⊢ x✝ ∈ ↑(↑(map f) (Ici a)) ↔ x✝ ∈ ↑(Ici (↑f a))",
"state_before": "α : Type u_1\nβ : Type u_2\... | [
1108,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.liftRel_swap_iff | [
{
"state_after": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_2\nδ : Type u_1\nr r₁ r₂ : α → γ → Prop\ns s₁ s₂ : β → δ → Prop\na : α\nb : β\nc : γ\nd : δ\nx : α ⊕ β\ny : γ ⊕ δ\nh : LiftRel s r (swap x) (swap y)\n⊢ LiftRel r s (swap (swap x)) (swap (swap y))",
"state_before": "α : Type u\nα'... | [
454,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_inv_mul_swap | [] | [
142,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.extraction_of_frequently_atTop | [
{
"state_after": "ι : Type ?u.58128\nι' : Type ?u.58131\nα : Type ?u.58134\nβ : Type ?u.58137\nγ : Type ?u.58140\nP : ℕ → Prop\nh : ∀ (a : ℕ), ∃ b, b > a ∧ P b\n⊢ ∃ φ, StrictMono φ ∧ ∀ (n : ℕ), P (φ n)",
"state_before": "ι : Type ?u.58128\nι' : Type ?u.58131\nα : Type ?u.58134\nβ : Type ?u.58137\nγ : Type ?... | [
470,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_pushoutLeftPushoutInrIso_inv | [] | [
2219,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2214,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_sup_comap_of_surjective | [] | [
1580,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1579,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.sub_apply | [] | [
492,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.DominatedFinMeasAdditive.add_measure_left | [] | [
253,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.vertex_mem_convexHull_iff | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.42000\ninst✝² : OrderedRing 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nK : SimplicialComplex 𝕜 E\ns t : Finset E\nx : E\nhx : x ∈ vertices K\nhs : s ∈ K.faces\nh : x ∈ ↑(convexHull 𝕜).toOrderHom ↑s\n⊢ x ∈ s",
"state_before": "𝕜 : Type u_2\... | [
175,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_sub_comm | [] | [
105,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_inj | [] | [
550,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_eq_of_forall_ge_of_forall_gt_exists_lt | [] | [
621,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Data/Multiset/Range.lean | Multiset.card_range | [] | [
44,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | covariant_le_iff_contravariant_lt | [] | [
303,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | IsGLB.mul_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.132337\nα : Type u_1\nβ : Type ?u.132343\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\ns : Set α\nha : 0 ≤ a\nhs : IsGLB s b\n⊢ IsGLB ((fun b => b * a) '' s) (b * a)",
"tactic": "simpa [mul_comm] using hs.mul_left ha"
}
] | [
668,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_zero | [] | [
230,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.star_mul_self | [] | [
115,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.pow | [
{
"state_after": "case zero\nR : Type u_1\nS : Type ?u.11283\nM : Type u_2\na b : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\nra : IsSMulRegular M a\n⊢ IsSMulRegular M (a ^ Nat.zero)\n\ncase succ\nR : Type u_1\nS : Type ?u.11283\nM : Type u_2\na b : R\ns : S\ninst✝¹ : Monoid R\ninst✝ : MulAction R M\nra... | [
159,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Basic.lean | nhds_basis_opens | [
{
"state_after": "α : 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⊢ HasBasis (⨅ (s : Set α) (_ : s ∈ {s | a ∈ s ∧ IsOpen s}), 𝓟 s) (fun s => a ∈ s ∧ IsOpen s) fun s => s",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns s₁... | [
866,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.minpoly.eval₂' | [] | [
202,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.bot_lt_coe_ennreal | [] | [
558,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Formula.inf_semanticallyEquivalent_not_sup_not | [] | [
574,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_apply_ne' | [] | [
444,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/GroupTheory/Commensurable.lean | Commensurable.equivalence | [] | [
64,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/Complex/Circle.lean | expMapCircle_zero | [
{
"state_after": "no goals",
"state_before": "⊢ ↑(↑expMapCircle 0) = ↑1",
"tactic": "rw [expMapCircle_apply, ofReal_zero, MulZeroClass.zero_mul, exp_zero, Submonoid.coe_one]"
}
] | [
131,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_eq_zero_iff | [] | [
453,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Topology/Instances/Irrational.lean | isGδ_irrational | [] | [
42,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
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