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/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.le_mul_iff_one_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.87217\ninst✝² : LE α\ninst✝¹ : MulOneClass α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\nha : MulLECancellable a\n⊢ a ≤ a * b ↔ a * 1 ≤ a * b",
"tactic": "rw [mul_one]"
}
] | [
1650,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1647,
11
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.congToClass_empty | [
{
"state_after": "case a\nz : ZFSet\n⊢ congToClass ∅ z ↔ ∅ z",
"state_before": "⊢ congToClass ∅ = ∅",
"tactic": "ext z"
},
{
"state_after": "case a\nz : ZFSet\n⊢ ¬setOf (fun y => ↑y ∈ ∅) z",
"state_before": "case a\nz : ZFSet\n⊢ congToClass ∅ z ↔ ∅ z",
"tactic": "simp only [congToClass, ... | [
1576,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1573,
1
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Mathlib/Topology/Constructions.lean | Dense.prod | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.63807\nδ : Type ?u.63810\nε : Type ?u.63813\nζ : Type ?u.63816\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\ns : Set α\nt : Set β\... | [
795,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_eq_self | [] | [
1998,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1994,
1
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Mathlib/Data/Fin/Basic.lean | Fin.pred_mk_succ | [
{
"state_after": "no goals",
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"tactic": "simp only [ext_iff, coe_pred, add_tsub_cancel_right]"
}
] | [
1524,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformly.tendsto_comp | [] | [
964,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
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Mathlib/Order/Monotone/Basic.lean | injective_of_le_imp_le | [] | [
563,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
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Mathlib/Algebra/Group/Commute.lean | Commute.all | [] | [
140,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_lt_top_of_isCompact | [] | [
1529,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
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Mathlib/Topology/List.lean | List.tendsto_removeNth | [
{
"state_after": "α : Type u_1\nβ : Type ?u.54838\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nx✝ : ℕ\n⊢ Tendsto (fun l => removeNth l x✝) (pure []) (𝓝 (removeNth [] x✝))",
"state_before": "α : Type u_1\nβ : Type ?u.54838\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nx✝ : ℕ\n⊢ Tend... | [
159,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt_neg_one | [
{
"state_after": "no goals",
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"tactic": "rwa [one_div_neg_one_eq_neg_one] at this"
}
] | [
896,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.real_toNNReal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.994446\nγ : Type ?u.994449\nδ : Type ?u.994452\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ\nhf : Integrable f\n⊢ HasFiniteIntegral fun x => ↑(Real.toNNReal (f x))",
"st... | [
828,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
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Mathlib/Data/List/Sublists.lean | List.sublists_append | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nl₁ l₂ : List α\n⊢ foldr (fun a r => List.bind r fun l => [l, a :: l]) (foldr (fun a r => List.bind r fun l => [l, a :: l]) [[]] l₂) l₁ =\n do\n let x ← foldr (fun a r => List.bind r fun l => [l, a :: l]) [[]] l₂\n map (fun x_1 => x_1 ++ x) (foldr (f... | [
166,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Analysis/LocallyConvex/Bounded.lean | NormedSpace.isVonNBounded_iff | [
{
"state_after": "𝕜 : Type u_2\n𝕜' : Type ?u.246833\nE : Type u_1\nE' : Type ?u.246839\nF : Type ?u.246842\nι : Type ?u.246845\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\n⊢ Bornology.IsVonNBounded 𝕜 s ↔ ∃ r, s ⊆ Metric.closedBall 0 r",
"st... | [
297,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.closure_induction | [
{
"state_after": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\ns : Set K\np : K → Prop\nx : K\nh : x ∈ closure s\nHs : ∀ (x : K), x ∈ s → p x\nH1 : p 1\nHadd : ∀ (x y : K), p x → p y → p (x + y)\nHneg : ∀ (x : K), p x → p (-x)\nHinv : ∀ (x : K), p x → p x⁻¹\nHmul : ∀ ... | [
745,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sup_lt_of_lt_sdiff_right | [
{
"state_after": "α : Type u\nβ : Type ?u.43541\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nh : x < z \\ y\nhyz : y ≤ z\n⊢ x ⊔ y < z \\ y ⊔ y",
"state_before": "α : Type u\nβ : Type ?u.43541\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nh : x < z \\ y\nhyz : y ≤ z\n⊢ x ⊔ y < z",
"tactic": "r... | [
485,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | infinite_basis_le_maximal_linearIndependent | [] | [
449,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.638693\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t✝ s t : SignedMeasure α\nμ : Measure α\ninst✝¹ : HaveLebesgueDecomposition s μ\ninst✝ : HaveLebesgueDecomposition t μ\n⊢ s + t = singularPart s μ + singularPart t μ + withDensityᵥ μ (rnDeriv s μ + rnDeriv t μ)",
... | [
1121,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_add_erase | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → AddZeroClass (β i)\ni : ι\nf : Π₀ (i : ι), β i\n⊢ ↑(single i (↑f i) + erase i f) i = ↑f i",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι →... | [
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96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.head | [] | [
386,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_single_apply | [] | [
1052,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isPredLimit | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : PartialOrder α\ninst✝² : PredOrder α\na b : α\nC : α → Sort ?u.21462\ninst✝¹ : IsPredArchimedean α\ninst✝ : NoMaxOrder α\n⊢ ¬IsPredLimit a",
"tactic": "simp"
}
] | [
413,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.inv_iInf | [] | [
204,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.toCocone_ι_app_mk | [] | [
139,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.eq_of_bisim | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nR : Computation α → Computation α → Prop\nbisim : IsBisimulation R\ns₁ s₂ : Computation α\nr : R s₁ s₂\n⊢ ↑s₁ = ↑s₂",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Computation α → Computation α → Prop\nbisim : IsBisimulation R\ns₁ s₂ :... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
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Mathlib/Analysis/Convex/Star.lean | starConvex_empty | [] | [
104,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.hasIntegral | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\nh : Inte... | [
245,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_add_tsum_compl | [] | [
774,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_set | [] | [
203,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_atTop_zero | [
{
"state_after": "α : Type ?u.81159\nβ : Type u_1\nγ : Type ?u.81165\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\ninst✝¹ : Nonempty β\ninst✝ : SemilatticeSup β\nf : β → ℝ≥0∞\n⊢ (∀ (ib : ℝ≥0∞), 0 < ib → ∃ ia, ∀ (x : β), x ∈ Ici ia → f x ∈ Iic ib) ↔\n ∀ (ε : ℝ≥0∞), ε > 0 → ∃ N, ∀ (n : β), ... | [
303,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
11
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.mul_integral_comp_mul_right | [] | [
251,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.basisFun_apply | [
{
"state_after": "no goals",
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
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] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjointAux_adjointAux | [
{
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99,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Data/Complex/Exponential.lean | isCauSeq_of_mono_bounded | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15452\ninst✝³ : Ring β\ninst✝² : LinearOrderedField α\ninst✝¹ : Archimedean α\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → α\na : α\nm : ℕ\nham : ∀ (n : ℕ), n ≥ m → abs' (f n) ≤ a\nhnm : ∀ (n : ℕ), n ≥ m → f n ≤ f (Nat.succ n)\n⊢ ↑(-{ val := fun n => -f n, prope... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atTop_isGLB | [
{
"state_after": "no goals",
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"tactic": "convert ... | [
120,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_le | [] | [
83,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.tsub_eq_of_eq_add_rev | [
{
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"tactic": "rw [add_comm, h]"
}
] | [
298,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_univ_of_noncompact | [
{
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"tactic": "simp [diam]"
}
] | [
2673,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | Filter.EventuallyEq.hasDerivAtFilter_iff | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
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] |
Mathlib/LinearAlgebra/Charpoly/Basic.lean | LinearMap.minpoly_dvd_charpoly | [] | [
84,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.add_tsub_cancel_left | [] | [
308,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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Mathlib/Data/List/Func.lean | List.Func.equiv_trans | [] | [
236,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Std/Data/List/Lemmas.lean | List.Sublist.eq_of_length | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ l₁✝ l₂✝ : List α✝\na : α✝\ns : l₁✝ <+ l₂✝\nh : length (a :: l₁✝) = length (a :: l₂✝)\n⊢ a :: l₁✝ = a :: l₂✝",
"tactic": "rw [s.eq_of_length (succ.inj h)]"
}
] | [
418,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
415,
1
] |
Mathlib/Analysis/PSeries.lean | Real.summable_one_div_nat_pow | [
{
"state_after": "no goals",
"state_before": "p : ℕ\n⊢ (Summable fun n => 1 / ↑n ^ ↑p) ↔ 1 < p",
"tactic": "simp only [one_div, Real.summable_nat_pow_inv]"
}
] | [
218,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Set/Finite.lean | Set.union_finset_finite_of_range_finite | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → Finset β\nh : Set.Finite (range f)\n⊢ Set.Finite (⋃ (x : Finset β) (_ : x ∈ range fun a => f a), ↑x)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → Finset β\nh : Set.Finite (range f)\n⊢ Set.Finite (⋃ (a : α... | [
1017,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.concyclic_pair | [] | [
232,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/List/AList.lean | AList.lookup_erase_ne | [] | [
251,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.bot_coprod_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.59384\nδ : Type ?u.59387\nι : Sort ?u.59390\nf : Filter α\ng : Filter β\n⊢ Filter.coprod ⊥ ⊥ = ⊥",
"tactic": "simp"
}
] | [
489,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | PontryaginDual.map_one | [] | [
461,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | Real.coe_fib_eq' | [
{
"state_after": "⊢ Set.EqOn (fun n => ↑(Nat.fib n)) (fun n => (φ ^ n - ψ ^ n) / sqrt 5) ↑(Finset.range fibRec.order)\n\ncase hu\n\n⊢ LinearRecurrence.IsSolution fibRec fun n => ↑(Nat.fib n)\n\ncase hv\n\n⊢ LinearRecurrence.IsSolution fibRec fun n => (φ ^ n - ψ ^ n) / sqrt 5",
"state_before": "⊢ (fun n => ↑... | [
231,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Order/CompleteLattice.lean | IsLUB.sSup_eq | [] | [
152,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Int/Parity.lean | Int.two_dvd_ne_zero | [] | [
91,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.continuous | [] | [
135,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
11
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.IsFixedPt.comp | [] | [
63,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.r_one_pow_n | [
{
"state_after": "n : ℕ\n⊢ r ↑n = r 0",
"state_before": "n : ℕ\n⊢ r 1 ^ n = 1",
"tactic": "rw [r_one_pow, one_def]"
},
{
"state_after": "case e_a\nn : ℕ\n⊢ ↑n = 0",
"state_before": "n : ℕ\n⊢ r ↑n = r 0",
"tactic": "congr 1"
},
{
"state_after": "no goals",
"state_before": "cas... | [
144,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Order/WithBot.lean | WithBot.unbot'_bot | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.ι_sndSigmaMap | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nI : MultispanIndex C\ninst✝¹ : HasCoproduct I.left\ninst✝ : HasCoproduct I.right\nb : I.L\n⊢ Sigma.ι I.left b ≫ sndSigmaMap I = snd I b ≫ Sigma.ι I.right (sndFrom I b)",
"tactic": "simp [sndSigmaMap]"
}
] | [
308,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Order/WellFounded.lean | WellFounded.lt_succ_iff | [
{
"state_after": "case mp\nα : Type u_1\nr : α → α → Prop\nwo : IsWellOrder α r\nx : α\nh : ∃ y, r x y\ny : α\n⊢ r y (WellFounded.succ (_ : WellFounded r) x) → r y x ∨ y = x\n\ncase mpr\nα : Type u_1\nr : α → α → Prop\nwo : IsWellOrder α r\nx : α\nh : ∃ y, r x y\ny : α\n⊢ r y x ∨ y = x → r y (WellFounded.succ (... | [
133,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.curry_uncurry | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_homothety_center | [] | [
69,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.mem_mk | [] | [
171,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.split_iff_of_iso | [
{
"state_after": "case mp\nC : Type u_2\ninst✝ : Category C\nX X' : C\nφ : X ≅ X'\np : X ⟶ X\np' : X' ⟶ X'\nhpp' : p ≫ φ.hom = φ.hom ≫ p'\n⊢ (∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p) → ∃ Y' i' e', i' ≫ e' = 𝟙 Y' ∧ e' ≫ i' = p'\n\ncase mpr\nC : Type u_2\ninst✝ : Category C\nX X' : C\nφ : X ≅ X'\np : X ⟶ X\np' : X' ⟶ ... | [
156,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_add | [] | [
358,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_mul_left | [] | [
1039,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.prodMonoidal_leftUnitor_hom_fst | [
{
"state_after": "case mk\nC : Type u\n𝒞 : Category C\ninst✝⁴ : MonoidalCategory C\nC₁ : Type u₁\ninst✝³ : Category C₁\ninst✝² : MonoidalCategory C₁\nC₂ : Type u₂\ninst✝¹ : Category C₂\ninst✝ : MonoidalCategory C₂\nfst✝ : C₁\nsnd✝ : C₂\n⊢ (λ_ (fst✝, snd✝)).hom.fst = (λ_ (fst✝, snd✝).fst).hom",
"state_befor... | [
628,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_norm_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.118286\nE : Type u_2\nF : Type ?u.118292\nG : Type ?u.118295\nE' : Type ?u.118298\nF' : Type u_3\nG' : Type ?u.118304\nE'' : Type ?u.118307\nF'' : Type ?u.118310\nG'' : Type ?u.118313\nR : Type ?u.118316\nR' : Type ?u.118319\n𝕜 : Type ... | [
697,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean | Matrix.Nondegenerate.eq_zero_of_ortho | [] | [
38,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.837134\nβ : Type ?u.837137\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ ENNReal.toReal a⁻¹ = (ENNReal.toReal a)⁻¹",
"tactic": "simp only [ENNReal.toReal, toNNReal_inv, NNReal.coe_inv]"
}
] | [
2322,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2321,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean | TopCat.Presheaf.isSheaf_iff_isSheafEqualizerProducts | [] | [
562,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_comm_le | [] | [
124,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_eq_nil | [
{
"state_after": "case mp\nn : ℕ\nh : factors n = []\n⊢ n = 0 ∨ n = 1\n\ncase mpr\nn : ℕ\nh : n = 0 ∨ n = 1\n⊢ factors n = []",
"state_before": "n : ℕ\n⊢ factors n = [] ↔ n = 0 ∨ n = 1",
"tactic": "constructor <;> intro h"
},
{
"state_after": "case mp.zero\nh : factors zero = []\n⊢ zero = 0 ∨ ze... | [
134,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasLimitsOfShape_of_equivalence | [] | [
267,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_strict_mono_left | [
{
"state_after": "k : Type u_2\nE : Type u_1\nPE : Type ?u.9072\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup E\ninst✝¹ : Module k E\ninst✝ : OrderedSMul k E\na a' b b' : E\nr r' : k\nha : a < a'\nhr : r < 1\n⊢ (1 - r) • a + r • b < (1 - r) • a' + r • b",
"state_before": "k : Type u_2\nE : Type u_1\... | [
61,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Computability/Partrec.lean | Computable.vector_tail | [] | [
386,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.toMatrix_injective | [
{
"state_after": "k : Type ?u.21960\nl : Type ?u.21963\nm : Type u_2\nn : Type u_1\nα : Type v\ninst✝² : DecidableEq n\ninst✝¹ : MonoidWithZero α\ninst✝ : Nontrivial α\nf g : m ≃. n\n⊢ toMatrix f = toMatrix g → f = g",
"state_before": "k : Type ?u.21960\nl : Type ?u.21963\nm : Type u_2\nn : Type u_1\nα : Ty... | [
148,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.89974\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nμ : VectorMeasure α ℝ≥0∞\nh : s ≪ᵥ μ\n⊢ totalVariation s ≪ VectorMeasure.ennrealToMeasure μ\n\ncase mpr\nα : Type u_1\nβ : Type ?u.89974\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nμ : VectorMeasure ... | [
534,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.monotone | [] | [
151,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.Nodup.le_dedup_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14659\ninst✝ : DecidableEq α\ns t : Multiset α\nhno : Nodup s\n⊢ s ≤ Multiset.dedup t ↔ s ≤ t",
"tactic": "simp [le_dedup, hno]"
}
] | [
145,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | CompactSpace.uniformEquicontinuous_of_equicontinuous | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.48697\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\nι : Type u_1\nF : ι → β → α\ninst✝ : CompactSpace β\nh : Continuous (↑UniformFun.ofFun ∘ Function.swap F)\n⊢ UniformEquicontinuous F",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.4... | [
273,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_prod | [] | [
259,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_preimage_le | [
{
"state_after": "R : Type u_1\nR₂ : Type u_2\nK : Type ?u.14881\nM : Type u_3\nM₂ : Type u_4\nV : Type ?u.14890\nS : Type ?u.14893\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R₂... | [
128,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffOn.pi | [] | [
380,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt | [
{
"state_after": "case a\nR : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.399378\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q✝ p q : MvPolynomial σ R\nh : totalDegree q < totalDegree p\n⊢ totalDegree (p + q) ≤ totalDegree p\n\ncase a\nR : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.39937... | [
675,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_union_left | [] | [
164,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.invFun_comp | [] | [
467,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.smul_mk_zero | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.3133\nP : Type ?u.3136\nE : Type ?u.3139\nα : Type u_3\nβ✝ : Type ?u.3145\ninst✝⁶ : SMul M α\ninst✝⁵ : SMul M β✝\ninst✝⁴ : SMul N α\ninst✝³ : SMul N β✝\na✝ : M\nx : α × β✝\nβ : Type u_1\ninst✝² : Monoid M\ninst✝¹ : AddMonoid β\ninst✝ : ... | [
82,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.mem_toAddSubgroup | [] | [
532,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_congr | [
{
"state_after": "α : Type ?u.349670\nβ : Type ?u.349673\nγ : Type ?u.349676\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no₁ : Ordinal\nf : (a : Ordinal) → a < o₁ → Ordinal\n⊢ blsub o₁ f = blsub o₁ fun a h => f a (_ : a < o₁)",
"state_before": "α : Type ?u.349670\nβ : Type ?u.349673\nγ : Type ?u.3... | [
1802,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Mathlib/Data/List/Sort.lean | List.mergeSort_cons_cons | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\na b : α\nl l₁ l₂ : List α\nh : split (a :: b :: l) = (l₁, l₂)\n⊢ mergeSort r (a :: b :: l) = merge r (mergeSort r l₁) (mergeSort r l₂)",
"tactic": "simp only [mergeSort, h]"
}
] | [
372,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_ofSubtype | [] | [
289,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_empty | [] | [
1392,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.pointwise_smul_le_pointwise_smul_iff | [] | [
430,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_symm | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_bUnion | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns : Set (Set R)\n⊢ zeroLocus (⋃ (s' : Set R) (_ : s' ∈ s), s') = ⋂ (s' : Set R) (_ : s' ∈ s), zeroLocus s'",
"tactic": "simp only [zeroLocus_iUnion]"
}
] | [
349,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_bit0 | [] | [
388,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Measurable.nat_floor | [] | [
82,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_pi_div_two_sub | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ cos (↑π / 2 - x) = sin x",
"tactic": "rw [← cos_neg, neg_sub, cos_sub_pi_div_two]"
}
] | [
1295,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Dense.eq_of_inner_left | [] | [
956,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_add | [] | [
112,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.leftOp_id | [] | [
392,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
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