file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_le_of_le | [] | [
463,
30
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_toExpr_go | [
{
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706,
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_le_of_le_right | [] | [
407,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Mathlib/CategoryTheory/Limits/FullSubcategory.lean | CategoryTheory.Limits.hasLimit_of_closed_under_limits | [] | [
115,
53
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111,
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Mathlib/Data/Set/Basic.lean | Set.inter_symmDiff_distrib_right | [] | [
2119,
35
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2118,
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Mathlib/Order/FixedPoints.lean | OrderHom.isLeast_lfp_le | [] | [
96,
36
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Icc_mem_nhds | [] | [
257,
46
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256,
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Mathlib/Analysis/Convex/Basic.lean | Convex.affine_image | [
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Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries_antitone | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nn : ℕ\nx : G\nhx : x ∈ lowerCentralSeries G (n + 1)\n⊢ x ∈ lowerCentralSeries G n",
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"tactic": "refine... | [
323,
86
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315,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mem_def | [] | [
116,
76
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Mathlib/Algebra/Module/Basic.lean | Convex.combo_self | [
{
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99,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/List/Card.lean | List.card_insert_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.26060\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\na : α\nas : List α\nh : ¬a ∈ as\n⊢ card (List.insert a as) = card as + 1",
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}
] | [
96,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/Data/Finset/Preimage.lean | Finset.prod_preimage' | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : CommMonoid β\nf : α → γ\ninst✝ : DecidablePred fun x => x ∈ Set.range f\ns : Finset γ\nhf : InjOn f (f ⁻¹' ↑s)\ng : γ → β\nthis : DecidableEq γ\n⊢ ∏ x in preimage s f hf, g (f x) = ∏ x in filter (fun x => x ∈ Set.range f) s, g x",
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152,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Data/Set/Lattice.lean | Set.prod_iUnion | [
{
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1762,
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1760,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Embedding.map_adj_iff | [] | [
1778,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1777,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciInf_iff | [] | [
519,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_eq_zero | [] | [
489,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_max | [] | [
1168,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
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Mathlib/Algebra/Category/Mon/FilteredColimits.lean | MonCat.FilteredColimits.colimit_mul_mk_eq | [
{
"state_after": "case mk\nJ : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ MonCat\ninst✝ : IsFiltered J\ny : (j : J) × ↑(F.obj j)\nk : J\ng : y.fst ⟶ k\nj₁ : J\nx : ↑(F.obj j₁)\nf : { fst := j₁, snd := x }.fst ⟶ k\n⊢ M.mk F { fst := j₁, snd := x } * M.mk F y =\n M.mk F { fst := k, snd := ↑(F.map f) { fst := j₁... | [
224,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp₂ | [] | [
859,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_eq_zero_iff | [] | [
725,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/Order/Filter/Extr.lean | IsMaxOn.isExtr | [] | [
174,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/Topology/Connected.lean | IsPreconnected.preimage_of_closed_map | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.26506\nπ : ι → Type ?u.26511\ninst✝¹ : TopologicalSpace α\ns✝ t u✝ v✝ : Set α\ninst✝ : TopologicalSpace β\ns : Set β\nhs : IsPreconnected s\nf : α → β\nhinj : Injective f\nhf : IsClosedMap f\nu v : Set α\nhu : IsClosed u\nhv : IsClosed v\nhsuv : f ⁻¹' s ⊆ u ... | [
402,
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.fromSubtype_toSubtype | [
{
"state_after": "J : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nf : J → C\ninst✝¹ : HasBiproduct f\np : J → Prop\ninst✝ : HasBiproduct (Subtype.restrict p f)\nj : Subtype p\n⊢ (fromSubtype f p ≫ toSubtype f p) ≫ π (Subtype.restrict p f) j =\n 𝟙 (⨁ Subtype.restrict p f) ≫ π (Subty... | [
654,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_lt_one | [
{
"state_after": "case intro\nz : ℝ\nhz : 0 < z\nx : ℝ≥0\nhx : ↑x < 1\n⊢ ↑x ^ z < 1",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx : x < 1\nhz : 0 < z\n⊢ x ^ z < 1",
"tactic": "lift x to ℝ≥0 using ne_of_lt (lt_of_lt_of_le hx le_top)"
},
{
"state_after": "case intro\nz : ℝ\nhz : 0 < z\nx : ℝ≥0\nhx : x < ... | [
668,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.ext | [] | [
93,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_mono | [] | [
1378,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.exists_edist_lt_of_hausdorffEdist_lt | [] | [
314,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Complex.hasFDerivAt_cpow | [] | [
70,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/RingTheory/TensorProduct.lean | LinearMap.baseChange_sub | [
{
"state_after": "case a.h.h\nR : Type u_4\nA : Type u_1\nB : Type ?u.473826\nM : Type u_2\nN : Type u_3\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Ring B\ninst✝⁴ : Algebra R B\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf g : M →ₗ[R] N\... | [
319,
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316,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.iSup_lt | [
{
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"tactic": "rwa [(#ι).lift_id]"
}
] | [
377,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommFoldr_cons | [
{
"state_after": "case h\nF : Type ?u.2553\nι : Type ?u.2556\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.2565\nf : α → β → β\nop : α → α → α\na : α\nb : β\na✝ : List α\nh : Set.Pairwise {x | x ∈ a ::ₘ Quotient.mk (List.isSetoid α) a✝} fun x y => ∀ (b : β), f x (f y b) = f y (f x b)\nh' : Set.Pairwise {x | x ∈ Quot... | [
70,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.IsSubordinate.toPartitionOfUnity | [] | [
489,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
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Mathlib/Combinatorics/Hall/Finite.lean | HallMarriageTheorem.hall_cond_of_restrict | [
{
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"state_before": "ι✝ : Type u\nα : Type v\ninst✝¹ : DecidableEq α\nt✝ : ι✝ → Finset α\ninst✝ : Fintype ι✝\nι : Type u\nt : ι → Finset α\ns : Finset ι\nht : ∀ (s : Finset ι), card s ≤ card (Finset.biUnion s t)\ns' : Finset ↑↑s\n⊢ card s' ≤ card (Finset.biUnion s' fun a' => t ↑a')"... | [
136,
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Mathlib/Data/Finset/Basic.lean | Finset.coe_pair | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.108687\nγ : Type ?u.108690\ninst✝ : DecidableEq α\ns t u v : Finset α\na✝ b✝ a b x✝ : α\n⊢ x✝ ∈ ↑{a, b} ↔ x✝ ∈ {a, b}",
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1124,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.add_right | [
{
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268,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
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Mathlib/Topology/Algebra/UniformGroup.lean | UniformCauchySeqOn.div | [
{
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533,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/PNat/Prime.lean | PNat.Coprime.factor_eq_gcd_left | [
{
"state_after": "a b m n : ℕ+\ncop : Coprime m n\nam : gcd a m = a\nbn : b ∣ n\n⊢ a = gcd (a * b) m",
"state_before": "a b m n : ℕ+\ncop : Coprime m n\nam : a ∣ m\nbn : b ∣ n\n⊢ a = gcd (a * b) m",
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},
{
"state_after": "a b m n : ℕ+\ncop : Coprime m n\n... | [
270,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_le_iff_degree_le | [] | [
224,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.zero_kroneckerTMul | [] | [
469,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_assoc' | [] | [
526,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
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Mathlib/Data/List/Basic.lean | List.foldl_ext | [
{
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"tactic": "induction l generalizing a with\n| nil => rfl\n| co... | [
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88
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Mathlib/Data/Finset/Basic.lean | List.toFinset_coe | [] | [
3243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3242,
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Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.mk'_apply | [] | [
689,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.congr_fun_ae | [] | [
148,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_lt_sqrt_iff | [] | [
60,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_single_of_pos | [] | [
932,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
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Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_right_injective | [
{
"state_after": "no goals",
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"tactic": "rw [← lxor'_cancel_left n m, ← lxor'_cancel_left n m', h]"
}
] | [
252,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_toLocalEquiv | [] | [
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6
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798,
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Mathlib/Data/Finset/Basic.lean | Finset.singleton_disjUnion | [] | [
1023,
42
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1021,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.snd_equivOfRightInverse | [] | [
2415,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2412,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_of_univ_subsingleton | [] | [
2380,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2379,
1
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Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Ioc | [] | [
161,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
11
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_iff_left_eq_or_right_mem_image_Ici | [
{
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692,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
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Mathlib/Data/Real/Irrational.lean | Irrational.rat_sub | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\n⊢ Irrational (↑q - x)",
"tactic": "simpa only [sub_eq_add_neg] using h.neg.rat_add q"
}
] | [
284,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_inj_real | [] | [
384,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_lt_mul_left | [] | [
260,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/Basic.lean | interior_empty | [] | [
329,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconcaveOn.inf | [] | [
122,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12543\nE : Type u_2\nF : Type u_3\nG : Type ?u.12552\nE' : Type ?u.12555\nF' : Type ?u.12558\nG' : Type ?u.12561\nE'' : Type ?u.12564\nF'' : Type ?u.12567\nG'' : Type ?u.12570\nR : Type ?u.12573\nR' : Type ?u.12576\n𝕜 : Type ?u.12579\n... | [
120,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | HasCompactMulSupport.eq_one_or_finiteDimensional | [
{
"state_after": "case pos\n𝕜 : Type u\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nF : Type w\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁸ : AddCommGroup F'\ninst✝⁷ : Module 𝕜 F'\ninst✝⁶ : TopologicalSpace F'... | [
511,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_comp_subtype | [
{
"state_after": "case mp\nι : Type u'\nι' : Type ?u.143047\nR : Type u_1\nK : Type ?u.143053\nM : Type u_2\nM' : Type ?u.143059\nM'' : Type ?u.143062\nV : Type u\nV' : Type ?u.143067\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Modul... | [
365,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_im | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.atTop_nsmul_neg_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nR : Type u_1\nl : Filter α\nf✝ : α → R\nr : R\ninst✝¹ : LinearOrderedAddCommGroup R\ninst✝ : Archimedean R\nf : α → ℕ\nhr : r < 0\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x => f x • r) l atBot",
"tactic": "simpa using hf.atTop_nsmul_const (neg_p... | [
228,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_comap | [] | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.augment_hom_zero | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX✝ X : CosimplicialObject C\nX₀ : C\nf : X₀ ⟶ X.obj [0]\nw : ∀ (i : SimplexCategory) (g₁ g₂ : [0] ⟶ i), f ≫ X.map g₁ = f ≫ X.map g₂\n⊢ f ≫ X.map (SimplexCategory.const [0] 0) = f",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ X : CosimplicialObject C\... | [
768,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | one_le_of_le_mul_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.16522\ninst✝² : MulOneClass α\ninst✝¹ : LE α\ninst✝ : ContravariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\nh : b ≤ a * b\n⊢ 1 * ?m.16901 h ≤ a * ?m.16901 h",
"tactic": "simpa only [one_mul]"
}
] | [
386,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_strictMono | [] | [
120,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | MultilinearMap.domCoprod_alternization_eq | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1240826\ninst✝²¹ : Semiring R\nM : Type ?u.1240832\ninst✝²⁰ : AddCommMonoid M\ninst✝¹⁹ : Module R M\nN : Type ?u.1240864\ninst✝¹⁸ : AddCommMonoid N\ninst✝¹⁷ : Module R N\nP : Type ?u.1240894\ninst✝¹⁶ : AddCommMonoid P\ninst✝¹⁵ : Module R P\nM' : Type... | [
1196,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.essentiallySmall_iff | [
{
"state_after": "case mp\nC✝ : Type u\ninst✝¹ : Category C✝\nC : Type u\ninst✝ : Category C\n⊢ EssentiallySmall C → Small (Skeleton C) ∧ LocallySmall C\n\ncase mpr\nC✝ : Type u\ninst✝¹ : Category C✝\nC : Type u\ninst✝ : Category C\n⊢ Small (Skeleton C) ∧ LocallySmall C → EssentiallySmall C",
"state_before"... | [
224,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Topology/Maps.lean | IsClosedMap.closure_image_subset | [] | [
495,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_cons_of_ne | [] | [
2359,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2358,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_mono | [] | [
841,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_mk | [] | [
498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsEulerian.card_filter_odd_degree | [
{
"state_after": "V : Type u_1\nG : SimpleGraph V\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nu v : V\np : Walk G u v\nht : IsEulerian p\n⊢ Finset.card (Finset.filter (fun v => Odd (degree G v)) Finset.univ) = 0 ∨\n Finset.card (Finset.filter (fun v => Odd (degree G v)) Finset.un... | [
163,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_mul_div_add | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.230000\nβ : Type ?u.230003\nγ : Type ?u.230006\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : b ≠ 0\n⊢ a < b * (a / b) + b",
"tactic": "simpa only [mul_succ] using lt_mul_succ_div a h"
}
] | [
893,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
src/lean/Init/Data/Nat/Power2.lean | Nat.mul2_isPowerOfTwo_of_isPowerOfTwo | [
{
"state_after": "no goals",
"state_before": "n : Nat\nh✝ : isPowerOfTwo n\nk : Nat\nh : n = 2 ^ k\n⊢ n * 2 = 2 ^ (k + 1)",
"tactic": "simp [h, Nat.pow_succ]"
}
] | [
34,
35
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
32,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec | [
{
"state_after": "case intro.intro.intro\nn : Type u_1\np : Type ?u.321806\nR : Type u₂\n𝕜 : Type u_2\ninst✝⁵ : Field 𝕜\ninst✝⁴ : DecidableEq n\ninst✝³ : DecidableEq p\ninst✝² : CommRing R\nr : ℕ\nM✝ : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜\ninst✝¹ : Fintype n\ninst✝ : Fintype p\nM : Matrix n n 𝕜\nL L' : Li... | [
692,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_injective_of_surjective | [] | [
906,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | concaveOn_of_deriv2_nonpos' | [] | [
1229,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Data/List/Basic.lean | List.takeI_length | [] | [
2326,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2324,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.eqOn | [] | [
1026,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Data/Fintype/Order.lean | Fintype.bddAbove_range | [
{
"state_after": "case intro\nα : Type u_1\ninst✝³ : Nonempty α\ninst✝² : Preorder α\ninst✝¹ : IsDirected α fun x x_1 => x ≤ x_1\nβ : Type u_2\ninst✝ : Fintype β\nf : β → α\nM : α\nhM : ∀ (i : β), f i ≤ M\n⊢ BddAbove (Set.range f)",
"state_before": "α : Type u_1\ninst✝³ : Nonempty α\ninst✝² : Preorder α\nin... | [
216,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | MulMemClass.mul_mem_add_closure | [
{
"state_after": "M : Type u_2\nA : Type ?u.259525\nB : Type ?u.259528\nR : Type u_1\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : SetLike M R\ninst✝ : MulMemClass M R\nS : M\nb : R\nhb : b ∈ AddSubmonoid.closure ↑S\n⊢ ∀ {a : R}, a ∈ AddSubmonoid.closure ↑S → a * b ∈ AddSubmonoid.closure ↑S",
"state_befor... | [
667,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.subset_interior_iff | [] | [
314,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.takeWhile | [] | [
1069,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1068,
1
] |
Mathlib/Algebra/Ring/Defs.lean | left_distrib | [] | [
83,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | mem_powers_iff_mem_range_order_of' | [] | [
269,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Combinatorics/Hindman.lean | Hindman.FP_partition_regular | [] | [
224,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.subtype_eq_val | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.mk_eq_top_iff | [] | [
800,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2867092\nR₁ : Type u_2\nR₂ : Type ?u.2867098\nM✝ : Type ?u.2867101\nM₁ : Type ?u.2867104\nM₂ : Type ?u.2867107\nM₁' : Type ?u.2867110\nM₂' : Type ?u.2867113\nn : Type ?u.2867116\nm : Type ?u.2867119\nn' : Type ?u.2867122\nm' : Type ?u.2867125\nι : Ty... | [
745,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_left_on_Ioc | [
{
"state_after": "case refine'_1\na b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\nhgg' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt g (g' x) x\nhcf : ContinuousOn f (Ioc a b)\nhcg : ContinuousOn g (Ioc a b)\nhg' : ∀ (x : ℝ), x ∈ Ioo a b → g' x ≠ 0\nhfb : f ... | [
145,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Control/Fold.lean | Traversable.toList_eq_self | [
{
"state_after": "α β γ : Type u\nt : Type u → Type u\ninst✝¹ : Traversable t\ninst✝ : IsLawfulTraversable t\nxs : List α\n⊢ ↑FreeMonoid.toList (List.traverse (Const.mk' ∘ FreeMonoid.of) xs) = xs",
"state_before": "α β γ : Type u\nt : Type u → Type u\ninst✝¹ : Traversable t\ninst✝ : IsLawfulTraversable t\nx... | [
391,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_of_false | [
{
"state_after": "ι : Type ?u.403432\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝ : CommMonoid β\np : α → Prop\nhp : DecidablePred p\nf g : α → β\nh : ∀ (x : α), x ∈ s → ¬p x\n⊢ (∏ x in ∅, f x) * ∏ x in s, g x = ∏ x in s, g x\n\nι : Type ?u.403432\nβ : Type u\nα : Type v\... | [
1005,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_right_lineMap | [] | [
133,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Std/Data/List/Lemmas.lean | List.mem_insert_of_mem | [] | [
911,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
910,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | MeasurableEmbedding.essSup_map_measure | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝ : CompleteLattice β\nγ : Type u_2\nmγ : MeasurableSpace γ\nf : α → γ\ng : γ → β\nhf : MeasurableEmbedding f\n⊢ essSup g (Measure.map f μ) ≤ essSup (g ∘ f) μ",
"state_before": "α : Type u_1\nβ : Type u_3... | [
242,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Hom/Group.lean | Monoid.coe_mul | [] | [
1337,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_le_iff | [] | [
212,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
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