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/CategoryTheory/EqToHom.lean | CategoryTheory.congrArg_cast_hom_left | [
{
"state_after": "case refl\nC : Type u₁\ninst✝ : Category C\nX Z : C\nq : X ⟶ Z\n⊢ cast (_ : (X ⟶ Z) = (X ⟶ Z)) q = eqToHom (_ : X = X) ≫ q",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y Z : C\np : X = Y\nq : Y ⟶ Z\n⊢ cast (_ : (Y ⟶ Z) = (X ⟶ Z)) q = eqToHom p ≫ q",
"tactic": "cases p"
},
... | [
82,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.of_map | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf✝ : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\nf : G →g G'\nhp : IsPath (Walk.map f p)\n⊢ IsPath p",
"tactic": "induction p with\n| nil => sim... | [
1550,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1541,
11
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.map_id | [
{
"state_after": "case h.mk.mk\nα : Type u_1\nβ : Type ?u.16100\nγ : Type ?u.16103\nx✝ : Sym2 α\nx y : α\n⊢ map id (Quot.mk Setoid.r (x, y)) = id (Quot.mk Setoid.r (x, y))",
"state_before": "α : Type u_1\nβ : Type ?u.16100\nγ : Type ?u.16103\n⊢ map id = id",
"tactic": "ext ⟨⟨x, y⟩⟩"
},
{
"state_... | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.not_limZero_of_not_congr_zero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : CauSeq β abv\nhf : ¬f ≈ 0\nh : LimZero f\n⊢ False",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : Is... | [
525,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_succ_bot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : OrderBot α\n⊢ a ≤ succ ⊥ ↔ a = ⊥ ∨ a = succ ⊥",
"tactic": "rw [le_succ_iff_eq_or_le, le_bot_iff, or_comm]"
}
] | [
547,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.zsmul_apply | [] | [
927,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
926,
1
] |
Mathlib/Dynamics/Ergodic/Conservative.lean | MeasureTheory.Conservative.iterate | [
{
"state_after": "case zero\nι : Type ?u.77532\nα : Type u_1\ninst✝ : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nhf : Conservative f μ\n⊢ Conservative (f^[Nat.zero]) μ\n\ncase succ\nι : Type ?u.77532\nα : Type u_1\ninst✝ : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nhf : Conservative f ... | [
207,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
11
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.factors_right_of_inf_factors | [] | [
415,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Nat/SuccPred.lean | Nat.succ_eq_succ | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.curryLeft_zero | [] | [
1260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.extract | [
{
"state_after": "b e : Pos\nx✝ : Substring\nh₁✝ : Valid x✝\nh₂ : Valid { str := toString x✝, startPos := b, stopPos := e }\nl m r : List Char\nh₁ : ValidFor l m r x✝\n⊢ Valid (Substring.extract x✝ b e)",
"state_before": "b e : Pos\nx✝ : Substring\nh₁ : Valid x✝\nh₂ : Valid { str := toString x✝, startPos :=... | [
1042,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1036,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.symm_apply_apply | [] | [
156,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_add_mul_self | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\n⊢ gcd m (n + k * m) = gcd m n",
"tactic": "simp [gcd_rec m (n + k * m), gcd_rec m n]"
}
] | [
174,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
173,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.WF.filterMap | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → Option γ\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nH : WF m\ng₁ : AssocList α β → List (α × γ) :=\n fun l => List.filterMap (fun x => Option.map (fun x_1 => (x.fst, x_1)) (f x.fst x.snd)) (AssocList.toList l)\nH1 :\n ∀ (l : AssocL... | [
347,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
308,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_eq_zero_iff_cos_eq | [
{
"state_after": "z : ℂ\n⊢ sin z = 0 ↔ 0 = sin z * sin z",
"state_before": "z : ℂ\n⊢ sin z = 0 ↔ cos z = 1 ∨ cos z = -1",
"tactic": "rw [← mul_self_eq_one_iff, ← sin_sq_add_cos_sq, sq, sq, ← sub_eq_iff_eq_add, sub_self]"
},
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ sin z = 0 ↔ 0... | [
1104,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Iio | [] | [
93,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
11
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_comm | [] | [
337,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.pow_succ_eq | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.8183\nN : Type u_1\nS : Type ?u.8189\nM₀ : Type ?u.8192\nM₁ : Type ?u.8195\nR : Type ?u.8198\nG : Type ?u.8201\nG₀ : Type ?u.8204\ninst✝⁷ : Mul M\ninst✝⁶ : Monoid N\ninst✝⁵ : Semigroup S\ninst✝⁴ : MulZeroClass M₀\ninst✝³ : MulOneClass M₁\ninst✝² : No... | [
85,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/RingTheory/FiniteType.lean | AddMonoidAlgebra.mem_closure_of_mem_span_closure | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : AddCommMonoid M\ninst✝ : Nontrivial R\nm : M\nS : Set M\nh : of' R M m ∈ span R ↑(Submonoid.closure (of' R M '' S))\n⊢ ↑Multiplicative.ofAdd m ∈ Submonoid.closure (↑Multiplicative.toAdd ⁻¹' S)",
"state_before": "R : Type u_1\nM : Ty... | [
413,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.toLin'_mul | [] | [
142,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_surjective | [] | [
654,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.ne_zero_of_c_ne_zero | [] | [
195,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/List/Range.lean | List.unzip_enumFrom_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ unzip (enumFrom n l) = (range' n (length l), l)",
"tactic": "simp only [enumFrom_eq_zip_range', unzip_zip, length_range']"
}
] | [
197,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.empty_infs | [] | [
310,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_subst | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.124912\nP : Type ?u.124915\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn✝ l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\nφ : Bounded... | [
462,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.bijective_iff_bijective_of_iUnion_eq_univ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.186792\nι : Sort ?u.186795\nι' : Sort ?u.186798\nι₂ : Sort ?u.186801\nκ : ι → Sort ?u.186806\nκ₁ : ι → Sort ?u.186811\nκ₂ : ι → Sort ?u.186816\nκ' : ι' → Sort ?u.186821\ns : Set β\nf : α → β\nU : ι → Set β\nhU : iUnion U = univ\n⊢ ((∀ (i : ι), Injective ... | [
1521,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.app_hom | [] | [
103,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Nat/SuccPred.lean | Nat.pred_iterate | [
{
"state_after": "a n : ℕ\n⊢ (pred ∘ pred^[n]) a = pred (a - n)",
"state_before": "a n : ℕ\n⊢ (pred^[n + 1]) a = a - (n + 1)",
"tactic": "rw [Function.iterate_succ', sub_succ]"
},
{
"state_after": "no goals",
"state_before": "a n : ℕ\n⊢ (pred ∘ pred^[n]) a = pred (a - n)",
"tactic": "exa... | [
69,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Logic/Basic.lean | ite_eq_iff' | [] | [
1143,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.mk_mul_mk | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_eq_of_associated_left | [] | [
867,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.invFun_surjective | [] | [
463,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_sup_left | [] | [
819,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.comp_assoc | [
{
"state_after": "case h\nα : Type u\nα' : Type ?u.65959\nβ : Type v\nβ' : Type ?u.65964\nγ : Type u_1\nφ : Type u_2\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ : OmegaCompletePartialOrder α'\nins... | [
730,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.set_support_mul_subset | [
{
"state_after": "α : Type u_1\np q : Perm α\nx : α\n⊢ x ∈ {x | ↑(p * q) x ≠ x} → x ∈ {x | ↑p x ≠ x} ∪ {x | ↑q x ≠ x}",
"state_before": "α : Type u_1\np q : Perm α\n⊢ {x | ↑(p * q) x ≠ x} ⊆ {x | ↑p x ≠ x} ∪ {x | ↑q x ≠ x}",
"tactic": "intro x"
},
{
"state_after": "α : Type u_1\np q : Perm α\nx :... | [
280,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.of_isBigO_im_re_rpow | [
{
"state_after": "l : Filter ℂ\nhre : Tendsto re l atTop\nr : ℝ\nhr : im =O[l] fun z => z.re ^ r\nn : ℕ\n⊢ (fun z => z.im ^ n) =O[l] fun z => (z.re ^ r) ^ n",
"state_before": "l : Filter ℂ\nhre : Tendsto re l atTop\nr : ℝ\nhr : im =O[l] fun z => z.re ^ r\nn : ℕ\n⊢ (fun z => z.im ^ ↑n) =O[l] fun z => (z.re ^... | [
71,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | RingTopology.toTopologicalSpace_injective | [
{
"state_after": "α : Type u_1\ninst✝ : Ring α\nf g : RingTopology α\na✝ : f.toTopologicalSpace = g.toTopologicalSpace\n⊢ f = g",
"state_before": "α : Type u_1\ninst✝ : Ring α\n⊢ Injective toTopologicalSpace",
"tactic": "intro f g _"
},
{
"state_after": "case mk\nα : Type u_1\ninst✝ : Ring α\ng ... | [
306,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Associates.prod_le_prod | [
{
"state_after": "α : Type u_1\nβ : Type ?u.42748\nγ : Type ?u.42751\nδ : Type ?u.42754\ninst✝ : CommMonoid α\np q : Multiset (Associates α)\nh : p ≤ q\nthis : DecidableEq (Associates α)\n⊢ Multiset.prod p ≤ Multiset.prod q",
"state_before": "α : Type u_1\nβ : Type ?u.42748\nγ : Type ?u.42751\nδ : Type ?u.4... | [
141,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.MonoOver.top_arrow | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.induction | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1629871\nι : Type ?u.1629874\nE : Type u_2\nF : Type ?u.1629880\n𝕜 : Type ?u.1629883\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\nhp_pos : p ≠ 0\nhp_ne_top : p ≠ ⊤\nP : { x // x ∈ simpleFunc E p μ ... | [
749,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_find | [
{
"state_after": "α : Type u_1\nβ : Type ?u.56687\nγ : Type ?u.56690\nδ : Type ?u.56693\nδ' : Type ?u.56696\nι : Sort uι\ns t u : Set α\ninst✝¹ : MeasurableSpace α\np : α → ℕ → Prop\ninst✝ : (x : α) → DecidablePred (p x)\nhp : ∀ (x : α), ∃ N, p x N\nhm : ∀ (k : ℕ), MeasurableSet {x | p x k}\nx : α\n⊢ Measurable... | [
457,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.aeSeq_eq_mk_ae | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nα : Type u_2\nβ : Type u_3\nγ : Type ?u.571614\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\nf : ι → α → β\nμ : MeasureTheory.Measure α\np : α → (ι → β) → Prop\ninst✝ : Countable ι\nhf : ∀ (i : ι), AEMeasurable (f i)\nhp : ∀ᵐ (x : α) ∂μ,... | [
118,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_mul_exp_add_div_pow_atTop | [
{
"state_after": "case inl\nα : Type ?u.33412\nx y z : ℝ\nl : Filter α\nb c : ℝ\nhb : 0 < b\n⊢ Tendsto (fun x => (b * exp x + c) / x ^ 0) atTop atTop\n\ncase inr\nα : Type ?u.33412\nx y z : ℝ\nl : Filter α\nb c : ℝ\nn : ℕ\nhb : 0 < b\nhn : n ≠ 0\n⊢ Tendsto (fun x => (b * exp x + c) / x ^ n) atTop atTop",
"s... | [
256,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.continuous | [] | [
1885,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1884,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.range_eq_iUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.199050\nγ : Type ?u.199053\nι✝ : Sort ?u.199056\nι' : Sort ?u.199059\nι₂ : Sort ?u.199062\nκ : ι✝ → Sort ?u.199067\nκ₁ : ι✝ → Sort ?u.199072\nκ₂ : ι✝ → Sort ?u.199077\nκ' : ι' → Sort ?u.199082\nι : Sort u_1\nf : ι → α\na : α\n⊢ a ∈ rang... | [
1670,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.bijective | [] | [
997,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | factorization_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : UniqueFactorizationMonoid α\ninst✝¹ : NormalizationMonoid α\ninst✝ : DecidableEq α\n⊢ factorization 0 = 0",
"tactic": "simp [factorization]"
}
] | [
2016,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2016,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective | [
{
"state_after": "C : Type u\ninst✝⁶ : Category C\ninst✝⁵ : HasColimits C\nX Y Z : TopCat\ninst✝⁴ : ConcreteCategory C\ninst✝³ : PreservesFilteredColimits (forget C)\ninst✝² : HasLimits C\ninst✝¹ : PreservesLimits (forget C)\ninst✝ : ReflectsIsomorphisms (forget C)\nF G : Sheaf C X\nf : F ⟶ G\nU : Opens ↑X\nh :... | [
585,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_comp_succ | [
{
"state_after": "case refine'_1\np q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh✝ : ∃ n, p n\nn✝ m : ℕ+\nh : ∃ n, p n\nh₂ : ∃ n, p (n + 1)\nh1 : ¬p 1\nn : ℕ+\n⊢ 1 < PNat.find h₂ + 1 → ¬p 1\n\ncase refine'_2\np q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh✝ : ∃ n, p n... | [
129,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderIsoOfFin_symm_apply | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.coe_zero | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.Ioi_eq_Ioc | [] | [
458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toAddMonoidHom_refl | [] | [
744,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_succ_comp_X_add_one | [
{
"state_after": "S : Type u\ninst✝ : Semiring S\nn : ℕ\n⊢ comp (pochhammer ℕ (n + 1)) (X + 1) = pochhammer ℕ (n + 1) + (↑n + 1) * comp (pochhammer ℕ n) (X + 1)",
"state_before": "S : Type u\ninst✝ : Semiring S\nn : ℕ\n⊢ comp (pochhammer S (n + 1)) (X + 1) = pochhammer S (n + 1) + (n + 1) • comp (pochhammer... | [
128,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.rangeIcc_apply | [] | [
122,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.symm | [] | [
1076,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_inj_right | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.12536\nγ : Type ?u.12539\na : α\ns✝ : Multiset α\nl₁ : List α\nt✝ : Multiset α\nl₂ : List α\n⊢ a ::ₘ Quot.mk Setoid.r l₁ = a ::ₘ Quot.mk Setoid.r l₂ ↔ Quot.mk Setoid.r l₁ = Quot.mk Setoid.r l₂",
"state_before": "α : Type u_1\nβ : Type ?u.12536\nγ : Typ... | [
151,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/SupIndep.lean | Finset.supIndep_univ_bool | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13543\nι : Type ?u.13546\nι' : Type ?u.13549\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\ns t : Finset ι\nf✝ : ι → α\ni : ι\nf : Bool → α\n⊢ true ≠ false",
"tactic": "simp only [Ne.def, not_false_iff]"
}
] | [
124,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.toOrderRingHom_injective | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.78843\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.78852\nδ : Type ?u.78855\ninst✝⁵ : NonAssocSemiring α\ninst✝⁴ : Preorder α\ninst✝³ : NonAssocSemiring β\ninst✝² : Preorder β\ninst✝¹ : NonAssocSemiring γ\ninst✝ : Preorder γ\nf g : α ≃+*o β\nh : toOrderR... | [
541,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Data/List/Basic.lean | List.modifyNthTail_modifyNthTail_le | [
{
"state_after": "case intro\nι : Type ?u.108113\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf g : List α → List α\nn : ℕ\nl : List α\nm : ℕ\nh : n ≤ n + m\n⊢ modifyNthTail g (n + m) (modifyNthTail f n l) = modifyNthTail (fun l => modifyNthTail g (n + m - n) (f l)) n l",
"state_before":... | [
1517,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.toMeasure_bind_apply | [] | [
195,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_bool | [] | [
364,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.den_mk | [
{
"state_after": "no goals",
"state_before": "n d : ℤ\n⊢ (n /. d).den = if d = 0 then 1 else Int.natAbs d / Int.gcd n d",
"tactic": "rcases d with ((_ | _) | _) <;>\n simp [divInt, mkRat, Rat.normalize, Nat.succPNat, Int.sign, Int.gcd, -Nat.cast_succ]"
}
] | [
72,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.a_of_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.286399\nF : Type ?u.286402\nK : Type ?u.286405\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nh : toPoly P = toPoly Q\n⊢ P.a = Q.a",
"tactic": "rw [← coeff_eq_a, h, coeff_eq_a]"
}
] | [
124,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_ofNat_of_zero_le | [
{
"state_after": "a : Int\nh : 0 ≤ a\nt : ∃ n, a - 0 = ↑n\n⊢ ∃ n, a = ↑n",
"state_before": "a : Int\nh : 0 ≤ a\n⊢ ∃ n, a = ↑n",
"tactic": "have t := le.dest_sub h"
},
{
"state_after": "a : Int\nh : 0 ≤ a\nt : ∃ n, a = ↑n\n⊢ ∃ n, a = ↑n",
"state_before": "a : Int\nh : 0 ≤ a\nt : ∃ n, a - 0 = ... | [
584,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
583,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.union | [] | [
318,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Init/Logic.lean | true_and_iff | [] | [
144,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Std/Data/String/Lemmas.lean | String.ext | [] | [
16,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
15,
8
] |
Mathlib/RingTheory/Noetherian.lean | fg_of_injective | [] | [
153,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow | [
{
"state_after": "case inl\nx✝ y z✝ x z : ℝ\nh : 0 ≤ x\nh₂ : 0 ≤ z\nh₁ : x ≤ x\n⊢ x ^ z ≤ x ^ z\n\ncase inr\nx✝ y✝ z✝ x y z : ℝ\nh : 0 ≤ x\nh₁ : x ≤ y\nh₂ : 0 ≤ z\nh₁' : x < y\n⊢ x ^ z ≤ y ^ z",
"state_before": "x✝ y✝ z✝ x y z : ℝ\nh : 0 ≤ x\nh₁ : x ≤ y\nh₂ : 0 ≤ z\n⊢ x ^ z ≤ y ^ z",
"tactic": "rcases e... | [
425,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.mul_num_den | [
{
"state_after": "a b c q r : ℚ\nhq' : ↑q.den ≠ 0\n⊢ q * r = q.num * r.num /. ↑(q.den * r.den)",
"state_before": "a b c q r : ℚ\n⊢ q * r = q.num * r.num /. ↑(q.den * r.den)",
"tactic": "have hq' : (↑q.den : ℤ) ≠ 0 := by have := den_nz q; simpa"
},
{
"state_after": "a b c q r : ℚ\nhq' : ↑q.den ≠ ... | [
456,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.cos_eq_cos_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ cos x = cos y ↔ ∃ k, y = 2 * ↑k * π + x ∨ y = 2 * ↑k * π - x",
"tactic": "exact_mod_cast @Complex.cos_eq_cos_iff x y"
}
] | [
221,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.coeFn_zero | [
{
"state_after": "case h\nΩ : Type u_1\ninst✝⁴ : MeasurableSpace Ω\nR : Type ?u.10659\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nx✝ : Set Ω\n⊢ ENNReal.toNNReal (↑↑↑0 x✝) = OfNat.ofNat 0 x✝",
"state_before": "Ω : Type u_1\ninst✝⁴ : Measur... | [
235,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_sum | [] | [
647,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.trans | [] | [
256,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Sign.lean | exists_signed_sum | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.148808\nα : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nf : α → ℤ\nβ : Type u_1\nt : Finset β\nsgn : β → SignType\ng : β → α\nhg : ∀ (b : β), g b ∈ s\nht : card t = ∑ a in s, Int.natAbs (f a)\nhf : ∀ (a : α), a ∈ s → (∑ b in t, if g b = a then ↑(... | [
518,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiffWithinAt.cexp | [] | [
174,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_subtype_le | [] | [
2984,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2983,
1
] |
Mathlib/Analysis/Convex/Combination.lean | convexHull_range_eq_exists_affineCombination | [
{
"state_after": "case refine'_1\nR : Type u_2\nE : Type u_1\nF : Type ?u.160371\nι : Type u_3\nι' : Type ?u.160377\nα : Type ?u.160380\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Modul... | [
297,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
src/lean/Init/Core.lean | ex_of_PSigma | [] | [
1050,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1049,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.mk_nat_cast | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.uniformIntegrable_congr_ae | [] | [
760,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_pmap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.8249\np : α → Prop\nf✝ : (a : α) → p a → β\nx✝ : Option α\ng : β → γ\nf : (a : α) → p a → β\nx : Option α\nH : ∀ (a : α), a ∈ x → p a\n⊢ Option.map g (pmap f x H) = pmap (fun a h => g (f a h)) x H",
"tact... | [
190,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_top_left | [] | [
244,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_zero | [] | [
1680,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1676,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.sup_eq_union | [] | [
1809,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1808,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.sum_range_pow_eq_bernoulli_sub | [
{
"state_after": "n p : ℕ\n⊢ ∑ x in range (p + 1), _root_.bernoulli x * ↑(Nat.choose (p + 1) x) * ↑n ^ (p + 1 - x) =\n ∑ i in range (succ p + 1), eval (↑n) (↑(monomial i) (_root_.bernoulli (succ p - i) * ↑(Nat.choose (succ p) i))) -\n _root_.bernoulli (succ p)\n\nn p : ℕ\n⊢ ↑p + 1 ≠ 0",
"state_befor... | [
179,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | Set.Countable.preimage_circleMap | [] | [
106,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.coe_to_lieSubalgebra_to_submodule | [] | [
259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.mk_symm | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/Image.lean | WithTop.range_eq | [] | [
1517,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1515,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝² : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμs_lim : Tendsto μs F (𝓝 μ)\nnonzero : μ ≠ 0\n⊢ ∀ (f : Ω →ᵇ ℝ≥0),\n Tendsto (fun i => testAgain... | [
477,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/Order.lean | nhds_induced | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type ?u.44623\nf✝ : α → β\nι : Sort ?u.44630\nT : TopologicalSpace α\nf : β → α\na : β\ns : Set β\n⊢ s ∈ 𝓝 a ↔ s ∈ comap f (𝓝 (f a))",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.44623\nf✝ : α → β\nι : Sort ?u.44630\nT : TopologicalSpace α\nf ... | [
841,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_add_of_distinct_val | [
{
"state_after": "K : Type ?u.1807321\nF : Type ?u.1807324\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.1807336\nΓ''₀ : Type ?u.1807339\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx y z : R\nh : ↑v x ≠ ↑v... | [
323,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_lt_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ -y < -x ↔ x < y",
"tactic": "rw [lt_iff_le_and_lf, lt_iff_le_and_lf, neg_le_neg_iff, neg_lf_neg_iff]"
}
] | [
1332,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_pow | [] | [
2244,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2243,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_lt_Iio | [] | [
179,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_reindex | [] | [
387,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_moveRight_of_le | [] | [
475,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.IsPrimitive.mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhp : IsPrimitive p\nhq : IsPrimitive q\n⊢ IsPrimitive (p * q)",
"tactic": "rw [isPrimitive_iff_content_eq_one, content_mul, hp.content_eq_one, hq.content_eq_on... | [
413,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
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