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/RingTheory/FractionalIdeal.lean | FractionalIdeal.div_spanSingleton | [
{
"state_after": "R : Type ?u.1525795\ninst✝⁷ : CommRing R\nS : Submonoid R\nP : Type ?u.1526002\ninst✝⁶ : CommRing P\ninst✝⁵ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝⁴ : CommRing R₁\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R₁ K\ninst✝¹ : IsFractionRing R₁ K\ninst✝ : IsDomain R₁\nJ ... | [
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1471,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasurableEmbedding.snormEssSup_map_measure | [] | [
926,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
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Mathlib/Data/Fin/Basic.lean | Fin.castSucc_castPred | [
{
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"tactic":... | [
2459,
19
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Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_mul_of_apply | [
{
"state_after": "case inl\nι : Type u_1\nσ : Type u_3\nS : Type ?u.414941\nR : Type u_2\ninst✝⁹ : DecidableEq ι\ninst✝⁸ : Semiring R\ninst✝⁷ : SetLike σ R\ninst✝⁶ : AddSubmonoidClass σ R\nA : ι → σ\ninst✝⁵ : CanonicallyOrderedAddMonoid ι\ninst✝⁴ : SetLike.GradedMonoid A\ninst✝³ : Sub ι\ninst✝² : OrderedSub ι\n... | [
271,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
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Mathlib/Order/MinMax.lean | min_lt_iff | [] | [
67,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.constants_mem | [] | [
163,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.map_nhds_eq_of_equiv | [] | [
612,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
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Mathlib/Data/Multiset/Basic.lean | Multiset.map_const | [] | [
1294,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
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Mathlib/CategoryTheory/Limits/Constructions/Over/Products.lean | CategoryTheory.Over.ConstructProducts.over_products_of_widePullbacks | [] | [
157,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_iInf | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.52313\nγ : Type ?u.52316\nι : Sort u_2\nκ : ι → Sort ?u.52324\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\nf : ι → UpperSet α\n⊢ ↑(⨅ (i : ι), f i) = ⋃ (i : ι), ↑(f i)",
"tactic": "simp [iInf]"
}
] | [
557,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
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Mathlib/Topology/Covering.lean | IsCoveringMap.isOpenMap | [] | [
173,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
11
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.isTopologicalBasis_basic_opens | [
{
"state_after": "case h_open\nR : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\n⊢ ∀ (u : Set (ProjectiveSpectrum 𝒜)), (u ∈ Set.range fun r => ↑(basicOpen 𝒜 r)) → IsOpen u\n\ncase h_nhds\nR : Type u_2\nA : Type u_1... | [
468,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
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Mathlib/GroupTheory/Finiteness.lean | Submonoid.FG.map | [
{
"state_after": "no goals",
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"tactic": "classical\n obtain ⟨s, rfl⟩ := h\n exact ⟨s.image e, by rw [Finset.coe... | [
150,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Analysis/SpecificLimits/Basic.lean | dist_le_of_le_geometric_of_tendsto₀ | [] | [
392,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/Topology/Inseparable.lean | inseparable_pi | [
{
"state_after": "no goals",
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335,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/GroupTheory/Perm/List.lean | List.zipWith_swap_prod_support | [
{
"state_after": "α : Type u_1\nβ : Type ?u.716493\ninst✝¹ : DecidableEq α\nl✝ : List α\nx✝ : α\ninst✝ : Fintype α\nl l' : List α\nx : α\nhx : x ∈ support (prod (zipWith swap l l'))\n⊢ x ∈ toFinset l ⊔ toFinset l'",
"state_before": "α : Type u_1\nβ : Type ?u.716493\ninst✝¹ : DecidableEq α\nl✝ : List α\nx : ... | [
197,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_inf_eq_map_inf_comap | [
{
"state_after": "case intro.intro.intro\nF : Type u_5\nR : Type u_1\nR₁ : Type ?u.928463\nR₂ : Type u_2\nR₃ : Type ?u.928469\nR₄ : Type ?u.928472\nS : Type ?u.928475\nK : Type ?u.928478\nK₂ : Type ?u.928481\nM : Type u_3\nM' : Type ?u.928487\nM₁ : Type ?u.928490\nM₂ : Type u_4\nM₃ : Type ?u.928496\nM₄ : Type ?... | [
1017,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_d_eq_zero' | [] | [
376,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/Analysis/Convex/Segment.lean | vadd_segment | [] | [
253,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
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] |
Mathlib/Data/Nat/PartENat.lean | PartENat.add_right_cancel_iff | [
{
"state_after": "case intro\na b : PartENat\nc : ℕ\nhc : ↑c ≠ ⊤\n⊢ a + ↑c = b + ↑c ↔ a = b",
"state_before": "a b c : PartENat\nhc : c ≠ ⊤\n⊢ a + c = b + c ↔ a = b",
"tactic": "rcases ne_top_iff.1 hc with ⟨c, rfl⟩"
},
{
"state_after": "case intro.refine_2.refine_2\na b : PartENat\nc : ℕ\nhc : ↑... | [
537,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
11
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sub_apply | [] | [
316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Std/Data/Fin/Lemmas.lean | Fin.mod_val | [] | [
12,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
11,
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Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.prod_mk | [
{
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1625,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
1
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Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.IsVonNBounded.smul_tendsto_zero | [
{
"state_after": "𝕜 : Type u_3\n𝕜' : Type ?u.156377\nE : Type u_1\nE' : Type ?u.156383\nF : Type ?u.156386\nι : Type u_2\n𝕝 : Type ?u.156392\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NontriviallyNormedField 𝕝\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : Module 𝕝 E\ninst✝¹ : TopologicalSpace E\ninst✝ :... | [
161,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_opposite_image_mul_preimage | [] | [
248,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | AlgHom.ext_of_adjoin_eq_top | [] | [
430,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometryEquiv.norm_iteratedFDeriv_comp_left | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
321,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.add_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.723564\nn : ZNum\n⊢ n + 0 = n",
"tactic": "cases n <;> rfl"
}
] | [
1164,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_const' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9600\nδ : Type ?u.9603\nδ' : Type ?u.9606\nι : Sort uι\ns t u : Set α\nf✝ g : α → β\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nf : β → α\nhf : ∀ (x y : β), f x = f y\n✝ : Nontrivial β\n⊢ Measurable f",
"state_... | [
277,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_diff_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.60813\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ici a \\ Ici b = Ico a b",
"tactic": "rw [diff_eq, compl_Ici, Ici_inter_Iio]"
}
] | [
1080,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
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Mathlib/Topology/Constructions.lean | continuous_quot_lift | [] | [
1154,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | map_exp_of_mem_ball | [
{
"state_after": "𝕂 : Type u_4\n𝔸 : Type u_2\n𝔹 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕂\ninst✝⁵ : NormedRing 𝔸\ninst✝⁴ : NormedRing 𝔹\ninst✝³ : NormedAlgebra 𝕂 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔹\ninst✝¹ : CompleteSpace 𝔸\nF : Type u_1\ninst✝ : RingHomClass F 𝔸 𝔹\nf : F\nhf : Continuous ↑f\nx : 𝔸... | [
318,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_congr | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nf₁ g₁ : R\nU : Opens ↑(PrimeSpectrum.Top R)\nhu : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₁ ∈ Ideal.primeCompl x.asIdeal\n⊢ const R f₁ g₁ U hu = const R f₁ g₁ U (_ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ U → g₁ ∈ Ideal.primeCompl x.asIdeal)",
"state_before": ... | [
393,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_natAdd_zero | [] | [
1454,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1452,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.nthHomSeq_add | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\nr s : R\nε : ℚ\nhε : ε > 0\n⊢ ∃ i,\n ∀ (j : ℕ), j ≥ i →... | [
552,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
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] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.of_denote_eq_cancelAux | [
{
"state_after": "no goals",
"state_before": "case zero\nctx : Context\nm₁ m₂ r₁ r₂ : Poly\nh : denote_eq ctx (cancelAux zero m₁ m₂ r₁ r₂)\n⊢ denote_eq ctx (List.reverse r₁ ++ m₁, List.reverse r₂ ++ m₂)",
"tactic": "assumption"
},
{
"state_after": "case succ\nctx : Context\nfuel : Nat\nih :\n ∀... | [
413,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
384,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_mul_zero | [] | [
650,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ofNat'_bit | [] | [
242,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.ext | [] | [
201,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM0.univ_supports | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\ninst✝¹ : Inhabited Γ\nΛ : Type u_2\ninst✝ : Inhabited Λ\nM : Machine₀\n⊢ Supports M Set.univ",
"tactic": "constructor <;> intros <;> apply Set.mem_univ"
}
] | [
1121,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_mapRange_index | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁✝ : ι → Type v₁\nβ₂✝ : ι → Type v₂\ndec : DecidableEq ι\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ninst✝⁴ : (i : ι) → Zero (β₁ i)\ninst✝³ : (i : ι) → Zero (β₂ i)\ninst✝² : (i : ι) → (x : β₁ i) → Decidable (x ≠ 0)\ninst✝¹ : (i : ι) → (x : β₂ i) → Decidable (x... | [
1723,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.elim | [] | [
324,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.cos_eq_one_iff_angle_eq_zero | [
{
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"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) = 1 ↔ angle x y = 0",
"tactic": "rw [... | [
348,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
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Mathlib/LinearAlgebra/Pi.lean | Submodule.iInf_comap_proj | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝² : Semiring R\nφ : ι → Type u_1\ninst✝¹ : (i : ι) → AddCommMonoid (φ i)\ninst✝ : (i : ι) → Module R (φ i)\nI : Set ι\np q : (i : ι) → Sub... | [
309,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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] |
Mathlib/Algebra/Quandle.lean | Rack.self_invAct_eq_iff_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Rack R\nx y : R\nh : op x ◃ op x = op y ◃ op y ↔ op x = op y\n⊢ x ◃⁻¹ x = y ◃⁻¹ y ↔ x = y",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ x ◃⁻¹ x = y ◃⁻¹ y ↔ x = y",
"tactic": "have h := @self_act_eq_iff_eq _ _ (op x) (op y)"
},
{
"state_after"... | [
320,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | lt_div_comm | [] | [
1008,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_to_submodule_eq_iff | [] | [
225,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_sup_closure_left | [] | [
259,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.mem_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7802\nγ : Type ?u.7805\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : DecidableEq α\na : α\n⊢ a ∈ sᶜ ↔ ¬a ∈ s",
"tactic": "simp [compl_eq_univ_sdiff]"
}
] | [
170,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.map_mul_of_coprime | [] | [
597,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_zero_of_ae_eq_zero | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.72393\nE : Type u_2\nF : Type ?u.72399\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nht_eq : ∀ᵐ (x : α) ∂μ, x ∈ t → f x = 0\nhf : AES... | [
280,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_sInf | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.Embedding.isElementary_of_exists | [
{
"state_after": "L : Language\nM : Type u_3\nN : Type u_4\nP : Type ?u.353970\nQ : Type ?u.353973\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nf : M ↪[L] N\nhtv :\n ∀ (n : ℕ) (φ : BoundedFormula L Empty (n + 1)) (x : Fin n → M) (a : N),\n BoundedFormula.Re... | [
313,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.finrank_eq_card_chooseBasisIndex | [
{
"state_after": "R : Type u\nM : Type v\nN : Type w\ninst✝⁹ : Ring R\ninst✝⁸ : StrongRankCondition R\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : Module.Free R M\ninst✝⁴ : Module.Finite R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : Module.Free R N\ninst✝ : Module.Finite R N\nthis : Non... | [
93,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W X✝ Y✝ Z✝ X Y Z X' : C\nf : X ⟶ X'\n⊢ (f ⊗ 𝟙 (Y ⊗ Z)) ≫ (α_ X' Y Z).inv = (α_ X Y Z).inv ≫ ((f ⊗ 𝟙 Y) ⊗ 𝟙 Z)",
"tactic": "rw [← ... | [
350,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_compl | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.90549\nγ : Type ?u.90552\ns t : Set α\ninst✝⁴ : DecidableEq α\ninst✝³ : Fintype ↑s\ninst✝² : Fintype ↑t\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑(sᶜ)\na✝ : α\n⊢ a✝ ∈ toFinset (sᶜ) ↔ a✝ ∈ toFinset sᶜ",
"state_before": "α : Type u_1\nβ : Type ?u.90549\nγ : Type... | [
724,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.one_lt_ncard | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.156100\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ 1 < ncard s ↔ ∃ a, a ∈ s ∧ ∃ b, b ∈ s ∧ a ≠ b",
"tactic": "simp_rw [ncard_eq_toFinset_card _ hs, Finset.one_lt_card, Finite.mem_toFinset]"
}
] | [
699,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | finrank_eq_zero_of_not_exists_basis_finset | [] | [
209,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.lastFun_from_append1_drop_last | [] | [
766,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Topology/Order.lean | induced_iInf | [] | [
444,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Finset/Pairwise.lean | Set.PairwiseDisjoint.image_finset_of_le | [
{
"state_after": "α : Type u_2\nι : Type u_1\nι' : Type ?u.1728\ninst✝² : DecidableEq ι\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\nhs : PairwiseDisjoint (↑s) f\ng : ι → ι\nhf : ∀ (a : ι), f (g a) ≤ f a\n⊢ PairwiseDisjoint (g '' ↑s) f",
"state_before": "α : Type u_2\nι : Type u_... | [
47,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Algebra/Invertible.lean | mul_left_inj_of_invertible | [] | [
305,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/MinMax.lean | min_max_distrib_left | [] | [
124,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.of_eq | [] | [
350,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.equivRange_apply | [] | [
983,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_image_ofInjective | [] | [
270,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.ext | [] | [
101,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_le_iff_le_comap | [] | [
828,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp_smul_const' | [] | [
430,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.exists_not_mem_col | [
{
"state_after": "case h.e'_2\nμ : YoungDiagram\nj : ℕ\n⊢ (fun i => ¬(i, j) ∈ μ.cells) = fun j_1 => ¬(j, j_1) ∈ transpose μ",
"state_before": "μ : YoungDiagram\nj : ℕ\n⊢ ∃ i, ¬(i, j) ∈ μ.cells",
"tactic": "convert μ.transpose.exists_not_mem_row j using 1"
},
{
"state_after": "no goals",
"sta... | [
360,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
11
] |
Mathlib/Topology/Order/Basic.lean | Filter.Tendsto.atBot_add | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : OrderTopology α\nl : Filter β\nf g : β → α\nC : α\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\n⊢ Tendsto (fun x => g x + f x) l atBot",
"state_before": "α : Type u\nβ : Type ... | [
1907,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1904,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.apply_inv_apply | [] | [
215,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.comp_lcm | [] | [
151,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.domRestrict_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.448336\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nS : Submodule R E\n⊢ (domRestr... | [
712,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Data/Prod/Lex.lean | Prod.Lex.lt_iff | [] | [
67,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | Submodule.exists_lieSubmodule_coe_eq_iff | [
{
"state_after": "case mp\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\np : Submodule R M\n⊢ (∃ N, ↑N = p) → ∀ (x : L) (m : M), m ∈ p → ⁅x, m⁆ ∈ p\n\ncase m... | [
297,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_closedBall | [] | [
481,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
9
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ext | [
{
"state_after": "case mk\nα : Type u\nα' : Type ?u.64625\nβ : Type v\nβ' : Type ?u.64630\nγ : Type ?u.64633\nφ : Type ?u.64636\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ : OmegaCompletePartialOr... | [
713,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
11
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | Set.Finite.nullMeasurableSet_sUnion | [] | [
387,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Quot.lean | Quot.induction_on₃ | [] | [
185,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_of_forall_lf | [] | [
442,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimit_bot | [] | [
68,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.sin | [] | [
158,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_monoidOf | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝¹ : CommMonoid N\nP : Type ?u.3281425\ninst✝ : CommMonoid P\nf : Submonoid.LocalizationMap S N\nx : M\n⊢ ↑(mulEquivOfQuotient f) (↑(Submonoid.LocalizationMap.toMap (monoidOf S)) x) = ↑(Subm... | [
1710,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.Pushforward.comp_eq | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.hasBasis_uniformity_of_basis_aux₁ | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type ?u.59454\nι : Type u_2\ns✝ s' : Set α\nx : α\np✝ : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\np : ι → Prop\ns : ι → Set (β × β)\nhb : HasBasis (𝓤 β) p s\nS : Set α\n⊢ HasBasis (comap (Prod.map (restrict S) (restrict S)) (𝓤 (↑S → β))) p... | [
641,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
11
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.mem_upperBounds_of_tendsto | [] | [
2077,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2074,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.cInf_mem | [] | [
58,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.isLittleO_of_lt_radius | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.114222\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinear... | [
209,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Std/Data/Int/DivMod.lean | Int.fdiv_one | [] | [
127,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
124,
9
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_le_div_left | [] | [
378,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_comp_map | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf✝ f : R →+* S₁\n⊢ RingHom.comp constantCoeff (map f) = RingHom.comp f constant... | [
1345,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_zipWith_left | [] | [
303,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.IsSymmetric.smul | [] | [
132,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.Continuous.inv | [] | [
122,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.rightAdjointUniq_trans_app | [
{
"state_after": "case a\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG G' G'' : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F ⊣ G'\nadj3 : F ⊣ G''\nx : D\n⊢ ((rightAdjointUniq adj1 adj2).hom.app x ≫ (rightAdjointUniq adj2 adj3).hom.app x).op =\n ((rightAdjointUniq adj1 adj3).hom.app x).op"... | [
301,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Order/LocallyFinite.lean | Ioc_ofDual | [
{
"state_after": "α : Type u_1\nβ : Type ?u.115387\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na✝ b✝ : α\na b : αᵒᵈ\n⊢ Ioc (↑ofDual a) (↑ofDual b) = Ico b a",
"state_before": "α : Type u_1\nβ : Type ?u.115387\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder ... | [
873,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_iff | [
{
"state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ Exact f g → f ≫ g = 0 ∧ kernel.ι g ≫ cokernel.π f = 0\n\ncase mpr\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ f ≫ g = 0 ∧ kernel.ι g ≫ cokernel.π f = 0 ... | [
85,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.equiv_toPEquiv_toMatrix | [] | [
185,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.mem_factors_iff_dvd | [] | [
148,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
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