file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Sym/Basic.lean | Sym.cons_swap | [] | [
131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_iff_not_affineIndependent | [
{
"state_after": "no goals",
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"tactic": "rw [collinear_iff_f... | [
457,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/LinearAlgebra/SModEq.lean | SModEq.def | [] | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.prob_add_prob_compl | [] | [
3221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3220,
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Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean | CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_id | [] | [
234,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Data/List/Infix.lean | List.dropLast_subset | [] | [
187,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xz_sub | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\n⊢ xz a1 (m - n) = xz a1 m * xz a1 n + ↑(Pell.d a1) * yz a1 m * -yz a1 n",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\n⊢ xz a1 (m - n) = xz a1 m * xz a1 n - ↑(Pell.d a1) * yz a1 m * yz a1 n",
"tactic": "rw [sub_eq_add_neg, ← mul_neg]"
... | [
389,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
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Mathlib/Computability/Reduce.lean | ComputablePred.computable_of_manyOneReducible | [
{
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"state_before": "α : T... | [
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54
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137,
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Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.mk'_arrow | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | measurable_smul_const | [] | [
109,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/LinearAlgebra/Projection.lean | LinearMap.IsProj.eq_conj_prodMap | [
{
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459,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Ioc | [
{
"state_after": "no goals",
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"tactic": "simp [← Ioi_inter_Iic]"
}
] | [
119,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Data/Int/Log.lean | Int.log_of_left_le_one | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/MeasureTheory/Function/Floor.lean | Int.measurable_ceil | [
{
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41,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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Mathlib/Algebra/GroupWithZero/Semiconj.lean | SemiconjBy.inv_right_iff₀ | [] | [
61,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.add_iSup | [
{
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"state_before": "α : Type ?u.136001\nβ : Type ?u.136004\nγ : Type ?u.1... | [
594,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
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Mathlib/Data/List/Cycle.lean | List.prev_reverse_eq_next | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nh : Nodup l\nk : ℕ\nhk : k < length l\nhx : nthLe l k hk ∈ l\n⊢ prev (reverse l) (nthLe l k hk) (_ : nthLe l k hk ∈ reverse l) = next l (nthLe l k hk) hx",
"state_before": "α : Type u_1\ninst✝ : Decidabl... | [
417,
12
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402,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_anti_mono_ideal | [] | [
245,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/List/Dedup.lean | List.sum_map_count_dedup_filter_eq_countp | [
{
"state_after": "case nil\nα : Type u\ninst✝ : DecidableEq α\np : α → Bool\n⊢ sum (map (fun x => count x []) (filter p (dedup []))) = countp p []\n\ncase cons\nα : Type u\ninst✝ : DecidableEq α\np : α → Bool\na : α\nas : List α\nh : sum (map (fun x => count x as) (filter p (dedup as))) = countp p as\n⊢ sum (ma... | [
135,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux | [
{
"state_after": "case refine'_1\nf g : CircleDeg1Lift\nx : ℕ → ℝ\nC : ℝ\nH : ∀ (n : ℕ), dist (↑(f ^ n) 0) (x n) ≤ C\n⊢ ℕ → ℝ\n\ncase refine'_2\nf g : CircleDeg1Lift\nx : ℕ → ℝ\nC : ℝ\nH : ∀ (n : ℕ), dist (↑(f ^ n) 0) (x n) ≤ C\n⊢ ∀ (t : ℕ), dist (transnumAuxSeq f t) (x (2 ^ t) / 2 ^ t) ≤ ?refine'_1 t\n\ncase r... | [
702,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
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Mathlib/Data/Fin/Basic.lean | Fin.strictMono_unique | [] | [
606,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
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Mathlib/Computability/Primrec.lean | Primrec.option_some_iff | [] | [
289,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.Sigma.ι_reindex_hom | [
{
"state_after": "β : Type w\nC : Type u\ninst✝² : Category C\nγ : Type v\nε : β ≃ γ\nf : γ → C\ninst✝¹ : HasCoproduct f\ninst✝ : HasCoproduct (f ∘ ↑ε)\nb : β\n⊢ ι (f ∘ ↑ε) b ≫\n (HasColimit.isoOfEquivalence (Discrete.equivalence ε)\n (Discrete.natIso fun x =>\n Iso.refl ((Discrete.func... | [
440,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_conj | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_rat_gt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\nx✝ y ε x : α\nn : ℕ\nh : x < ↑n\n⊢ x < ↑↑n",
"tactic": "rwa [Rat.cast_coe_nat]"
}
] | [
255,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.smul | [] | [
461,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
11
] |
Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_im_lt | [] | [
39,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
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Mathlib/Data/Fintype/Basic.lean | Fintype.choose_subtype_eq | [
{
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1124,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_smul_right | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\n𝕜₂ : Type ?u.53503\n𝕝 : Type ?u.53506\n𝕝₂ : Type ?u.53509\nE : Type u_1\nF : Type ?u.53515\nG : Type ?u.53518\nι : Type u_3\nι' : Type ?u.53524\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\nv : E\nU ... | [
156,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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] |
Mathlib/Data/Finset/Slice.lean | Finset.mem_slice | [] | [
143,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk | [] | [
245,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.mem_sup_right | [
{
"state_after": "R : Type u_1\nS✝ : Type ?u.151745\nM : Type u_2\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S✝\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S✝ M\ninst✝¹ : SMul S✝ R\ninst✝ : IsScalarTower S✝ R M\np q S T : Submodule R M\nthis : T ≤ S ⊔ T\n⊢ ∀ {x : M}, x ∈ T → x ∈ S ⊔ T",
"st... | [
287,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.range_finsetBasis | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : IsNoetherian K V\n⊢ Set.range ↑(finsetBasis K V) = Basis.ofVectorSpaceIndex K V",
"tactic": "rw [finsetBasis, Basis.range_reindex, Basis.range_ofVectorSpac... | [
106,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_inj | [
{
"state_after": "no goals",
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"tactic": "simp [h]"
}
] | [
119,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add_assoc | [
{
"state_after": "case c\nR : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\ny z : OreLocalization R S\nr₁ : R\ns₁ : { x // x ∈ S }\n⊢ r₁ /ₒ s₁ + y + z = r₁ /ₒ s₁ + (y + z)",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nx y z : OreLocalization R S... | [
655,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
11
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.mul_toPEquiv_toMatrix | [
{
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115,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_mul | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nf g : CauSeq ℚ abs\n⊢ mk (f * g) = mk f * mk g",
"tactic": "simp [mk, ← ofCauchy_mul]"
}
] | [
337,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/CategoryTheory/Preadditive/Generator.lean | CategoryTheory.Preadditive.isSeparating_iff | [
{
"state_after": "no goals",
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"tactic": "simpa only [Limits.comp_zero] us... | [
34,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
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] |
Mathlib/Algebra/Divisibility/Units.lean | isUnit_of_dvd_unit | [] | [
136,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_darts | [
{
"state_after": "no goals",
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"tactic": "induction p <;> simp [*]"
}
] | [
777,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Algebra/Invertible.lean | commute_invOf | [] | [
342,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
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Mathlib/Data/Set/Lattice.lean | Set.sInter_eq_iInter | [
{
"state_after": "no goals",
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... | [
1326,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_smul_real | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.680254\nG : Type ?u.680257\n𝕜 : Type ?u.680260\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : NormedSpace ℝ F'\ninst✝² ... | [
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Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.openEmbedding | [] | [
138,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Topology/Bases.lean | Embedding.secondCountableTopology | [] | [
894,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
11
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_vadd_const_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.121133\nP : Type u_3\nP' : Type ?u.121139\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx y z : V\n... | [
221,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Analysis/Convex/Combination.lean | mem_Icc_of_mem_stdSimplex | [] | [
479,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.apply_eq_zero | [
{
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999,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.lift_self | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type ?u.654027\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\nz : ℤ_[p]\n⊢ ↑(lift\n (_ :\n ∀ (... | [
666,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.30514\nf✝ : α ↪ β\ns : Finset α\nf : α ≃ β\np : α → Prop\ninst✝ : DecidablePred p\n⊢ map (Equiv.toEmbedding f) (filter p s) = filter (p ∘ ↑f.symm) (map (Equiv.toEmbedding f) s)",
"tactic": "simp only [filter_map, Funct... | [
189,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.isClosed_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8619\nσ : Type ?u.8622\nτ : Type ?u.8625\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : Set α\na : α\nthis : (a : Prop) → Decidable a\n⊢ (¬a ∈ s → ∃ b, a ∈ f F.F b ∧ ∀ (z : α), z ∈ f F.F b → ¬z ∈ s) ↔\n (∀ (b : F.σ), a ∈ f F.F b → ∃ z, z ∈ f F.F b ∩ s) → a ∈ s",
... | [
152,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.tsum_mul_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : ℝ≥0\nf : α → ℝ≥0\n⊢ ↑(∑' (x : α), a * f x) = ↑(a * ∑' (x : α), f x)",
"tactic": "simp only [coe_tsum, NNReal.coe_mul, tsum_mul_left]"
}
] | [
195,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
8
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_mul_mul_card_le_card_mul_mul_card_mul | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B C✝ A C : Finset α\n⊢ card (A * C) * card ∅ ≤ card (A * ∅) * card (∅ * C)\n\ncase inr\nα : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA✝ B✝ C✝ A B C : Finset α\nhB : Finset.Nonempty B\n⊢ card (A * C) * card B ... | [
160,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_eraseMin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nsize✝ sz : ℕ\nl' : Ordnode α\ny : α\nr' : Ordnode α\nx : α\nr : Ordnode α\n⊢ dual (eraseMin (node size✝ (node sz l' y r') x r)) = eraseMax (dual (node size✝ (node sz l' y r') x r))",
"tactic": "rw [eraseMin, dual_balanceR, dual_eraseMin (node s... | [
602,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_le_comap_iff_of_surjective | [] | [
495,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Computability/Ackermann.lean | ack_succ_zero | [
{
"state_after": "no goals",
"state_before": "m : ℕ\n⊢ ack (m + 1) 0 = ack m 1",
"tactic": "rw [ack]"
}
] | [
76,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.trans_eq_none | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\ng : β ≃. γ\na : α\n⊢ (∀ (a_1 : γ), ¬∃ b, b ∈ ↑f a ∧ a_1 ∈ ↑g b) ↔ ∀ (b : β) (c : γ), b ∈ ↑f a → ¬c ∈ ↑g b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\ng : β ≃. γ\na : α\n⊢ ↑(PEquiv.trans f g) a = ... | [
164,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_min'_iff | [] | [
1342,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_of_subset_zero | [
{
"state_after": "case inl\n𝕜 : Type ?u.34254\nE : Type u_1\nF : Type ?u.34260\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nt : Set E\na : ℝ\nh : ∅ ⊆ 0\n⊢ gauge ∅ = 0\n\ncase inr\n𝕜 : Type ?u.34254\nE : Type u_1\nF : Type ?u.34260\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nt : Set E\na : ℝ\nh : {0} ⊆ 0\n⊢... | [
128,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/RingTheory/TensorProduct.lean | TensorProduct.AlgebraTensorModule.lift_tmul | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.lift.map_hom | [
{
"state_after": "α✝ : Type u\nβ✝ : Type v\ninst✝² : AddCommGroup β✝\nf✝ : α✝ → β✝\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝¹ : AddCommGroup β\ninst✝ : AddCommGroup γ\na : FreeAbelianGroup α\nf : α → β\ng : β →+ γ\n⊢ ↑(AddMonoidHom.comp g (↑lift f)) a = ↑(↑lift (↑g ∘ f)) a",
"state_before": "α✝ : Typ... | [
136,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithBot.succ_unbot | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.61733\ninst✝² : Preorder α\ninst✝¹ : OrderBot α\ninst✝ : SuccOrder α\na : WithBot α\nha : a ≠ ⊥\n⊢ succ a ≠ ⊥",
"tactic": "induction a using WithBot.recBotCoe <;> simp"
}
] | [
1224,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.nndist_le_of_le | [
{
"state_after": "X : Type u_1\nY : Type u_2\nZ : Type ?u.903365\ninst✝¹ : PseudoMetricSpace X\ninst✝ : PseudoMetricSpace Y\nC r : ℝ≥0\nf : X → Y\nhf : HolderWith C r f\nx y : X\nd : ℝ≥0\nhd : nndist x y ≤ d\n⊢ nndist (f x) (f y) ≤ C * d ^ ↑r",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ?u.903365... | [
246,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/GroupTheory/Perm/Subgroup.lean | Equiv.Perm.sigmaCongrRightHom.card_range | [] | [
55,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.foldl_data_eq_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : List α\nacc : Array β\nF : Array β → α → Array β\nG : α → List β\nH : ∀ (acc : Array β) (a : α), (F acc a).data = acc.data ++ G a\n⊢ (List.foldl F acc l).data = acc.data ++ List.bind l G",
"tactic": "induction l generalizing a... | [
210,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
206,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.trans_apply | [] | [
280,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
9
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.isCompact | [] | [
333,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_piecewise_zero | [
{
"state_after": "case refine'_1\nα : Type u_1\nE : Type ?u.125245\nF : Type u_2\n𝕜 : Type ?u.125251\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\np : ℝ≥0∞\nG : Type ?u.125353\nF' : Type ?u.125356\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedAddCommGroup F'\ninst✝ :... | [
370,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_orderIso_refl | [] | [
452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.continuous_eval_const | [] | [
174,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.uniformInducing_iff | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.25437\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nf : α → β\n⊢ (∀ (i' : ℝ≥0∞),\n 0 < i' →\n ∃ i,\n 0 < i ∧\n ∀ (a b : α),\n (a, b) ∈ Prod.map f f ⁻¹' {p | edist p.fst p.snd < i} → (a, b) ∈ {p | e... | [
296,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.sameRay_map_iff | [] | [
182,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.unbounded_principal | [] | [
127,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.eq_true_of_not_eq_false | [] | [
83,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.bijOn_iInter | [] | [
1632,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1628,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_eq_inv_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.213054\nβ : Type ?u.213057\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a / b = b⁻¹ * a",
"tactic": "rw [div_eq_mul_inv, mul_comm]"
}
] | [
1330,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.singleton_smul_singleton | [] | [
165,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_of_ne_zero | [] | [
49,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/Max.lean | IsBot.mono | [] | [
301,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fast_fib_aux_bit_tt | [
{
"state_after": "n : ℕ\n⊢ (if true = true then\n ((binaryRec (fib 0, fib 1)\n (fun b x p =>\n if b = true then (p.snd ^ 2 + p.fst ^ 2, p.snd * (2 * p.fst + p.snd))\n else (p.fst * (2 * p.snd - p.fst), p.snd ^ 2 + p.fst ^ 2))\n n).snd ^\n ... | [
233,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Order/Lattice.lean | lt_sup_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : LinearOrder α\na b c d : α\n⊢ a < b ⊔ c ↔ a < b ∨ a < c",
"tactic": "exact ⟨fun h =>\n (le_total c b).imp\n (fun bc => by rwa [sup_eq_left.2 bc] at h)\n (fun bc => by rwa [sup_eq_right.2 bc] at h),\n fun h => h.elim lt... | [
858,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13421\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t✝ s₁ s₂ t₁ t₂ : Set α\nx : α\ns t : Set α\n⊢ 𝓝ˢ (s ∪ t) = 𝓝ˢ s ⊔ 𝓝ˢ t",
"tactic": "simp only [nhdsSet, image_union, sSup_union]"
}
] | [
135,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Int/Log.lean | Int.log_natCast | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\n⊢ log b ↑Nat.zero = ↑(Nat.log b Nat.zero)\n\ncase succ\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb n✝ : ℕ\n⊢ log b ↑(Nat.succ n✝) = ↑(Nat.log b (Nat.succ n✝))",
"sta... | [
81,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | IsBoundedLinearMap.contDiff | [
{
"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... | [
152,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsMatching.toEdge.surjective | [
{
"state_after": "case mk\nV : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nh : IsMatching M\ne : Sym2 V\nhe : e ∈ edgeSet M\n⊢ ∃ a, toEdge h a = { val := e, property := he }",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\nh : IsMatching M\n⊢ Function.Surjective (toEdge h)",
"tacti... | [
77,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_iff_cauchySeq_finset | [] | [
1093,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullback_of_right_iso | [] | [
1724,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1723,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.subset_congr_left | [] | [
103,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.coe_lift₂_symm_apply | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/BooleanAlgebra.lean | eq_compl_iff_isCompl | [
{
"state_after": "α : Type u\nβ : Type ?u.53845\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : x = yᶜ\n⊢ IsCompl (yᶜ) y",
"state_before": "α : Type u\nβ : Type ?u.53845\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : x = yᶜ\n⊢ IsCompl x y",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_... | [
618,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableWithinAt_snd | [] | [
298,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.cg_def | [] | [
111,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_sub | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ c d a b : α\n⊢ abs (a + -b) ≤ abs a + abs (-b)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ c d a b : α\n⊢ abs (a - b) ≤ abs a + abs b",
"tactic": "rw [sub_eq_add_neg, ← abs_neg b]"
},
{
"st... | [
281,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_congr | [] | [
490,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | MulOpposite.comap_unop_nhds | [] | [
85,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.minDegree_le_degree | [
{
"state_after": "case intro\nι : Sort ?u.290851\n𝕜 : Type ?u.290854\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w : V\ne : Sym2 V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv : V\nt : ℕ\nht : Finset.min (image (fun v => degree G v) univ) = ↑t\n⊢ minDegree G ≤ d... | [
1525,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_eq_update | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\ninst✝ : DecidableEq α\ni j x : α\n⊢ ↑(swap i j) x = update (update id j i) i j x",
"tactic": "rw [update_apply _ i j, update_apply _ j i, Equiv.swap_apply_def, id.def]"
}
] | [
1599,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1598,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.Iso.inv_hom | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝ : Category C\nX Y Z : C\nf✝ g : X ⟶ Y\nh : Y ⟶ Z\nf : X ≅ Y\n⊢ f.hom ≫ f.inv = 𝟙 X",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nf✝ g : X ⟶ Y\nh : Y ⟶ Z\nf : X ≅ Y\n⊢ inv f.hom = f.inv",
"tactic": "apply inv_eq_of_hom_inv_id"
},
{... | [
419,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_pow | [] | [
1171,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1169,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.map_post | [] | [
104,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
102,
1
] |
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