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 |
|---|---|---|---|---|---|---|
Std/Logic.lean | decide_eq_true_iff | [
{
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"tactic": "simp"
}
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522,
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Mathlib/Algebra/GroupPower/Basic.lean | div_pow | [
{
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"tactic": "simp only [div_eq_mul_inv, mul_pow, inv_pow]"
}
] | [
393,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_le_iff_of_neg | [] | [
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Mathlib/Order/Monotone/Basic.lean | Antitone.ne_of_lt_of_lt_int | [
{
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"state_before": "ι : Type ?u.46031\nα : Type u\nβ : Type v\nγ : Type w... | [
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77
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasStrictFDerivAt.isBigO_sub | [] | [
420,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | continuous_prod_of_continuous_lipschitz | [
{
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow | [
{
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533,
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Mathlib/Order/Filter/Pointwise.lean | Filter.top_pow | [
{
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"tactic": "rw [pow_succ, top_pow n.succ_ne_z... | [
718,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_sep | [
{
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"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "... | [
992,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
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Mathlib/Data/Sum/Basic.lean | Sum.update_elim_inl | [
{
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"tactic": "simp"
},
{
"state_after":... | [
279,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
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Mathlib/Analysis/Convex/Between.lean | Wbtw.swap_left_iff | [
{
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392,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_nonneg_restrict_of_forall_set_integral_nonneg_inter | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.le_arch | [
{
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"state_before": "d : ℕ\na : ℤ√↑d\n⊢ ∃ n, a ≤ ↑n",
"tactic": "obtain ⟨x, y, (h : a ≤ ⟨x, y⟩)⟩ : ∃ x y : ℕ, Nonneg (⟨x, y⟩ + -a) :=\n match -a with\n | ⟨Int.ofNat x, Int.ofNat y⟩ => ⟨0, 0, by tr... | [
782,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_bot | [] | [
385,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.associator_inv_app | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed_set_eq | [] | [
4083,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4081,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.trans | [
{
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596,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.of_s_of_int | [
{
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"state_before": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\na : ℤ\n⊢ ∀ (n : ℕ), Stream'.Seq.get? (of ↑a).s n = none",
... | [
293,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.piLpCongrLeft_single | [] | [
326,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Order/Filter/Basic.lean | Set.EqOn.eventuallyEq | [] | [
3115,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3114,
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr | [] | [
426,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
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Mathlib/Topology/UniformSpace/Cauchy.lean | cauchySeq_iff' | [] | [
229,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.whiskerLeft_iff | [
{
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"tactic": "simp"
}
] | [
417,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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src/lean/Init/SimpLemmas.lean | Bool.not_false | [
{
"state_after": "no goals",
"state_before": "⊢ (!false) = true",
"tactic": "decide"
}
] | [
125,
62
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
125,
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] |
Mathlib/Analysis/Calculus/Deriv/Slope.lean | hasDerivWithinAt_iff_tendsto_slope' | [
{
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"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Fi... | [
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Mathlib/GroupTheory/OrderOfElement.lean | powers_eq_zpowers | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Homology/ImageToKernel.lean | homology.comp_right_eq_comp_left | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_image | [
{
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"tactic": "simp only [infEdist, iInf_image, hΦ.edist_eq]"
}... | [
197,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_zero | [
{
"state_after": "no goals",
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"tactic": "rw [eq_comm, IsLoca... | [
353,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Logic.lean | subsingleton_iff_forall_eq | [] | [
756,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
755,
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Mathlib/Analysis/Normed/Group/Basic.lean | tendsto_norm_div_self | [
{
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Mathlib/Combinatorics/Quiver/Basic.lean | Prefunctor.ext | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
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Std/Data/Array/Lemmas.lean | Array.getD_eq_get? | [
{
"state_after": "α : Type u_1\na : Array α\nn : Nat\nd : α\n⊢ (if h : n < size a then a[n] else d) = Option.getD (if h : n < size a then some a[n] else none) d",
"state_before": "α : Type u_1\na : Array α\nn : Nat\nd : α\n⊢ getD a n d = Option.getD (get? a n) d",
"tactic": "simp [get?, getD]"
},
{
... | [
63,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Topology/Inseparable.lean | Inseparable.specializes | [] | [
276,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
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Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean | CategoryTheory.Limits.ι_colimitLimitIso_limit_π | [
{
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399,
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386,
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Mathlib/Data/Set/Finite.lean | Set.Infinite.exists_not_mem_finset | [] | [
1387,
47
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1384,
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Mathlib/Order/UpperLower/Basic.lean | IsLowerSet.union | [] | [
110,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Order/Antichain.lean | IsAntichain.preimage_embedding | [] | [
160,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Algebra/Ring/BooleanRing.lean | toBoolRing_ofBoolRing | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_copy | [] | [
98,
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_comp_le | [
{
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"tactic": "simp"
}
] | [
230,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.castLE_castLE | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.49784\nP : Type ?u.49787\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.49815\nn k : ℕ\nφ : BoundedFormula L α k\n⊢ ∀ {m n : ℕ} (km : k ≤ m) (mn : m ≤ n), castLE mn (castLE km φ)... | [
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28
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460,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | eq_orthogonalProjection_of_mem_orthogonal | [] | [
809,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
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Std/Data/Int/DivMod.lean | Int.add_mul_ediv_left | [] | [
174,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
172,
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] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.one_nonempty | [] | [
120,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.jointly_surjective' | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nx : colimit F\n⊢ ∃ j y, colimit.ι F j y = x",
"tactic": "exact jointly_surjective.{v, u} F (colimit.isColimit F) x"
}
] | [
377,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.nhds_coe_eq | [] | [
288,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.sin_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : ℂ\n⊢ sin θ ≠ 0 ↔ ∀ (k : ℤ), θ ≠ ↑k * ↑π",
"tactic": "rw [← not_exists, not_iff_not, sin_eq_zero_iff]"
}
] | [
63,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | neg_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2661\nγ : Type ?u.2664\ninst✝ : BooleanRing α\na b : α\n⊢ -a = -a + 0",
"tactic": "rw [add_zero]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2661\nγ : Type ?u.2664\ninst✝ : BooleanRing α\n... | [
85,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/NormedSpace/RieszLemma.lean | Metric.closedBall_infDist_compl_subset_closure | [
{
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118,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_map_right | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.465503\nr : α → β → Prop\np : γ → δ → Prop\ns : Multiset α\nt : Multiset γ\nf : γ → β\n⊢ Rel (flip fun a b => flip r (f a) b) s t ↔ Rel (fun a b => r a (f b)) s t",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.... | [
2772,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2770,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_topEquiv | [] | [
688,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_norm_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.984360\nδ : Type ?u.984363\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nhf : AEStronglyMeasurable f μ\n⊢ (Integrable fun a => ... | [
768,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.id_le | [] | [
1132,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_injective_of_surjective | [] | [
465,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.length_eq_map | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ Computation.IsBisimulation fun c1 c2 =>\n ∃ l s,\n c1 =\n Computation.corec\n (fun x =>\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum... | [
1253,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
] |
Mathlib/Order/Chain.lean | Flag.ext | [] | [
313,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_nonpos | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.18184\nι : Type ?u.18187\nα : Type u_1\nβ : Type ?u.18193\ninst✝¹ : OrderedRing α\ninst✝ : Nontrivial α\nn : ℤ\n⊢ ↑n ≤ 0 ↔ n ≤ 0",
"tactic": "rw [← cast_zero, cast_le]"
}
] | [
146,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Certificate.of_combine | [
{
"state_after": "no goals",
"state_before": "ctx : Context\ncs : Certificate\nh : PolyCnstr.denote ctx (combine cs) → False\n⊢ denote ctx cs",
"tactic": "match cs with\n| [] => simp [combine, PolyCnstr.denote, Poly.denote_eq] at h\n| (k, c)::cs =>\n simp [denote, combine] at *\n intro h'\n apply of_... | [
689,
14
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
682,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.smul | [] | [
1022,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Icc_iff_right | [] | [
123,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_eq_setToSimpleFunc | [] | [
695,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.comp_ι_eq | [
{
"state_after": "case H\nV : Type u_1\nW : Type u_2\nV₁ : Type ?u.501676\nV₂ : Type ?u.501679\nV₃ : Type ?u.501682\ninst✝⁷ : SeminormedAddCommGroup V\ninst✝⁶ : SeminormedAddCommGroup W\ninst✝⁵ : SeminormedAddCommGroup V₁\ninst✝⁴ : SeminormedAddCommGroup V₂\ninst✝³ : SeminormedAddCommGroup V₃\nf : NormedAddGrou... | [
899,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.biInf_apply | [
{
"state_after": "α : Type u_2\nι : Type u_1\nI : Set ι\nhI : Set.Nonempty I\nm : ι → OuterMeasure α\ns : Set α\nthis : Nonempty ↑I\n⊢ ↑(⨅ (i : ι) (_ : i ∈ I), m i) s =\n ⨅ (t : ℕ → Set α) (_ : s ⊆ iUnion t), ∑' (n : ℕ), ⨅ (i : ι) (_ : i ∈ I), ↑(m i) (t n)",
"state_before": "α : Type u_2\nι : Type u_1\nI... | [
1211,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_def' | [] | [
77,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Std/Logic.lean | or_self_right | [] | [
346,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
346,
9
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_min | [] | [
699,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.integrable | [] | [
257,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.desc_comp_inl_comp_inr | [
{
"state_after": "C : Type u\ninst✝² : Category C\nX✝ Y✝ W X Y Z : C\ninst✝¹ : HasBinaryCoproduct W Y\ninst✝ : HasBinaryCoproduct X Z\ng : W ⟶ X\ng' : Y ⟶ Z\n⊢ map g g' ≫ desc inl inr = map g g'",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ W X Y Z : C\ninst✝¹ : HasBinaryCoproduct W Y\ninst✝ : H... | [
875,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_Ioi_of_forall_Ioc | [
{
"state_after": "ι : Type ?u.4550285\nα : Type u_2\nβ✝ : Type ?u.4550291\nγ : Type ?u.4550294\nδ : Type ?u.4550297\nR : Type ?u.4550300\nm0 : MeasurableSpace α\ninst✝⁴ : MeasurableSpace β✝\ninst✝³ : MeasurableSpace γ\ninst✝² : MeasurableSpace δ\nf g✝ : α → β✝\nμ ν : MeasureTheory.Measure α\nβ : Type u_1\nmβ : ... | [
331,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.extendWith_single_zero | [
{
"state_after": "case h.none\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.661354\nα : Option ι → Type v\ninst✝¹ : DecidableEq ι\ninst✝ : (i : Option ι) → Zero (α i)\ni : ι\nx : α (some i)\n⊢ ↑(extendWith 0 (single i x)) none = ↑(single (some i) x... | [
1654,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1647,
1
] |
Mathlib/Topology/Algebra/Algebra.lean | algebraMapClm_toLinearMap | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_inf_map_of_injective | [] | [
580,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.algebraMap_eq_diagonal | [] | [
1320,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
Mathlib/NumberTheory/Zsqrtd/ToReal.lean | Zsqrtd.toReal_injective | [] | [
34,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.coe_int_div_eq_divInt | [
{
"state_after": "a b c : ℚ\nn d : ℤ\n⊢ n /. 1 / (d /. 1) = n /. d",
"state_before": "a b c : ℚ\nn d : ℤ\n⊢ ↑n / ↑d = n /. d",
"tactic": "repeat' rw [coe_int_eq_divInt]"
},
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn d : ℤ\n⊢ n /. 1 / (d /. 1) = n /. d",
"tactic": "exact d... | [
505,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.smul_eq_diagonal_mul | [
{
"state_after": "case a.h\nl : Type ?u.279030\nm : Type u_1\nn : Type u_2\no : Type ?u.279039\nm' : o → Type ?u.279044\nn' : o → Type ?u.279049\nR : Type ?u.279052\nS : Type ?u.279055\nα : Type v\nβ : Type w\nγ : Type ?u.279062\ninst✝² : NonUnitalNonAssocSemiring α\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nM... | [
1051,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Order/LocallyFinite.lean | Prod.uIcc_mk_mk | [] | [
1010,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | cauchyPowerSeries_apply | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nR : ℝ\nn : ℕ\nw : ℂ\n⊢ (w ^ n • (2 * ↑π * I)⁻¹ • ∮ (z : ℂ) in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z) =\n (2 * ↑π * I)⁻¹ • w ^ n • ∮ (z : ℂ) in C(c, R), (z - c)⁻¹ ^ n • (z - c... | [
538,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Order/Lattice.lean | Subtype.mk_sup_mk | [] | [
1389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.one_fst | [] | [
289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_eq_empty_of_subsingleton | [] | [
502,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_mono_right | [
{
"state_after": "case inl\nb n m : ℕ\nh : n ≤ m\nhb : b ≤ 1\n⊢ clog b n ≤ clog b m\n\ncase inr\nb n m : ℕ\nh : n ≤ m\nhb : 1 < b\n⊢ clog b n ≤ clog b m",
"state_before": "b n m : ℕ\nh : n ≤ m\n⊢ clog b n ≤ clog b m",
"tactic": "cases' le_or_lt b 1 with hb hb"
},
{
"state_after": "case inl\nb n ... | [
339,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.elim_comp_map | [] | [
251,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_Ioi_ae_eq_pi_Ici | [] | [
496,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.exists_companion | [] | [
214,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.not_all_isAtomic | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.109819\nP : Type ?u.109822\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.109850\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Na... | [
688,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Order/Atoms.lean | isAtomic_iff_forall_isAtomic_Iic | [] | [
303,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousOn.rpow_const | [] | [
322,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Std/Logic.lean | not_not_em | [] | [
245,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
245,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.col_apply | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_add_lt_left_of_lt_add | [
{
"state_after": "a b c : Int\nh : a < b + c\n⊢ a + -b < c",
"state_before": "a b c : Int\nh : a < b + c\n⊢ -b + a < c",
"tactic": "rw [Int.add_comm]"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : a < b + c\n⊢ a + -b < c",
"tactic": "exact Int.sub_left_lt_of_lt_add h"... | [
1093,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1091,
11
] |
Mathlib/Data/Nat/Parity.lean | Nat.Odd.of_mul_left | [] | [
165,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.subsumes_right | [] | [
93,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_apply | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.one_apply | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.isIntegral_trans | [] | [
1024,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Std/Data/Option/Lemmas.lean | Option.isSome_iff_exists | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nx : Option α✝\n⊢ isSome x = true ↔ ∃ a, x = some a",
"tactic": "cases x <;> simp [isSome]"
}
] | [
55,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
55,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.hσ'_naturality | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX✝ : SimplicialObject C\nq n m : ℕ\nhnm : ComplexShape.Rel c m n\nX Y : SimplicialObject C\nf : X ⟶ Y\nh : n + 1 = m\n⊢ f.app [n].op ≫ hσ' q n m hnm = hσ' q n m hnm ≫ f.app [m].op",
"state_before": "C : Type u_2\ninst✝¹ : Category C... | [
171,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
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