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/Order/Bounds/Basic.lean | lowerBounds_mono_mem | [] | [
204,
36
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203,
1
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Mathlib/Order/Concept.lean | extentClosure_iUnion | [] | [
116,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/LinearAlgebra/AffineSpace/Restrict.lean | AffineMap.restrict.linear_aux | [
{
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67,
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Mathlib/Data/List/Perm.lean | List.subperm_cons_erase | [
{
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780,
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Mathlib/Algebra/GroupPower/Order.lean | Right.pow_lt_one_iff | [] | [
360,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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Mathlib/MeasureTheory/Covering/DensityTheorem.lean | IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx y : α\nr : ℝ\nh : dist x y ≤ K * r\nrpos : 0 < r\nR : ℝ := s... | [
112,
54
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74,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffWithinAt.rpow_const_of_ne | [] | [
522,
35
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520,
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Mathlib/Data/Complex/Exponential.lean | Complex.sinh_zero | [
{
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"state_before": "x y : ℂ\n⊢ sinh 0 = 0",
"tactic": "simp [sinh]"
}
] | [
601,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
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Mathlib/LinearAlgebra/Basis.lean | Basis.mem_submodule_iff | [
{
"state_after": "ι : Type u_3\nι' : Type ?u.464742\nR : Type u_1\nR₂ : Type ?u.464748\nK : Type ?u.464751\nM : Type u_2\nM' : Type ?u.464757\nM'' : Type ?u.464760\nV : Type u\nV' : Type ?u.464765\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'... | [
590,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
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Mathlib/RingTheory/WittVector/StructurePolynomial.lean | eq_wittStructureInt | [
{
"state_after": "case h\np : ℕ\nR : Type ?u.1579762\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℤ\nφ : ℕ → MvPolynomial (idx × ℕ) ℤ\nh : ∀ (n : ℕ), ↑(bind₁ φ) (W_ ℤ n) = ↑(bind₁ fun i => ↑(rename (Prod.mk i)) (W_ ℤ n)) Φ\nk : ℕ\n⊢ φ k = wittStructureInt p Φ k",
"state... | [
330,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.add_mem_centralizer | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nS T : Set M\na b : M\ninst✝ : Distrib M\nha : a ∈ centralizer S\nhb : b ∈ centralizer S\nc : M\nhc : c ∈ S\n⊢ c * (a + b) = (a + b) * c",
"tactic": "rw [add_mul, mul_add, ha c hc, hb c hc]"
}
] | [
88,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioo_of_Ioc | [] | [
212,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_inl | [] | [
969,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_prodMap' | [
{
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234,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/Algebra/Category/GroupCat/Limits.lean | AddCommGroupCat.kernelIsoKer_hom_comp_subtype | [
{
"state_after": "case w\nJ : Type v\ninst✝ : SmallCategory J\nG H : AddCommGroupCat\nf : G ⟶ H\nx✝ : ↑(kernel f)\n⊢ ↑((kernelIsoKer f).hom ≫ AddSubgroup.subtype (AddMonoidHom.ker f)) x✝ = ↑(kernel.ι f) x✝",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nG H : AddCommGroupCat\nf : G ⟶ H\n⊢ (kernelIso... | [
454,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.bot_eq_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nB : C\n⊢ (IsInitial.uniqueUpToIso initialIsInitial HasZeroObject.zeroIsInitial).hom ≫ 0 = initial.to B",
"tactic": "simp"
}... | [
338,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_mono_left | [] | [
81,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/GroupTheory/Solvable.lean | Equiv.Perm.not_solvable | [
{
"state_after": "G : Type ?u.94765\nG' : Type ?u.94768\ninst✝¹ : Group G\ninst✝ : Group G'\nf : G →* G'\nX : Type u_1\nhX : 5 ≤ Cardinal.mk X\nh : IsSolvable (Perm X)\n⊢ False",
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235,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_subtype | [] | [
1737,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1734,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.mem_baseSet_trivializationAt | [] | [
211,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr_set | [
{
"state_after": "case intro.intro.intro\nH : Type u_1\nM : Type ?u.1376\nH' : Type ?u.1379\nM' : Type ?u.1382\nX : Type ?u.1385\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : ... | [
91,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRel.symm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α → Prop\nH : Symmetric R\ns1 s2 : WSeq α\nh : Function.swap (LiftRel R) s2 s1\n⊢ LiftRel R s2 s1",
"tactic": "rwa [LiftRel.swap, H.swap_eq] at h"
}
] | [
567,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.locality | [] | [
197,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.sub_zero | [] | [
1645,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1644,
11
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.smul_singleton | [
{
"state_after": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nM✝ N : Submodule R A\nm n a : A\nM : Submodule R A\n⊢ ↑Set.up {a} • span R ↑M = map (LinearMap.mulLeft R a) M",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA :... | [
664,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.mkContinuousOfExistsBound_apply | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_midpoint_midpoint_le' | [] | [
225,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.all | [
{
"state_after": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ ψ : BoundedFormula L α (n + 1)\nh : SemanticallyEquivalent T φ ψ\n⊢ ∀ (M : ModelType T) (v : α → ↑M) (xs : Fin n → ↑M),\n (∀ (a : ↑M), BoundedFormula.Realize φ v (Fin.snoc xs a)) ↔ ∀ (a : ↑M), BoundedFormula.Realize ψ v (Fin.snoc xs a)",
... | [
468,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Small/Basic.lean | small_lift | [] | [
65,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.coe_vanishingIdeal | [
{
"state_after": "case h\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nt : Set (PrimeSpectrum R)\nf : R\n⊢ f ∈ ↑(vanishingIdeal t) ↔ f ∈ {f | ∀ (x : PrimeSpectrum R), x ∈ t → f ∈ x.asIdeal}",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nt : Set (Prime... | [
168,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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] |
Mathlib/Order/CompleteLattice.lean | iInf_range' | [] | [
736,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.inter_comm | [] | [
1832,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1831,
1
] |
Std/Logic.lean | exists_eq_or_imp | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ (∃ a, (a = a' ∨ q a) ∧ p a) ↔ p a' ∨ ∃ a, q a ∧ p a",
"tactic": "simp only [or_and_right, exists_or, exists_eq_left]"
}
] | [
474,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
473,
9
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_neg | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ (↑(-r)).re = (-↑r).re ∧ (↑(-r)).im = (-↑r).im",
"tactic": "simp [ofReal']"
}
] | [
257,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | inf_iSup₂_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort u_1\ninst✝ : Frame α\ns t : Set α\na✝ b : α\nf : (i : ι) → κ i → α\na : α\n⊢ (a ⊓ ⨆ (i : ι) (j : κ i), f i j) = ⨆ (i : ι) (j : κ i), a ⊓ f i j",
"tactic": "simp only [inf_iSup_eq]"
}
] | [
114,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Set/Basic.lean | Set.symmDiff_subset_union | [] | [
2101,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2100,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_xor'_odd | [
{
"state_after": "no goals",
"state_before": "m n✝ n : ℤ\n⊢ Xor' (Even n) (Odd n)",
"tactic": "cases even_or_odd n with\n| inl h => exact Or.inl ⟨h, even_iff_not_odd.mp h⟩\n| inr h => exact Or.inr ⟨h, odd_iff_not_even.mp h⟩"
},
{
"state_after": "no goals",
"state_before": "case inl\nm n✝ n :... | [
78,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.normalize_gcd | [
{
"state_after": "no goals",
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"tactic": "simp [gcd_def]"
}
] | [
184,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexRange_repr_self | [] | [
483,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | linearEquiv_det_rotation | [
{
"state_after": "no goals",
"state_before": "a : { x // x ∈ circle }\n⊢ ↑LinearEquiv.det (↑rotation a).toLinearEquiv = 1",
"tactic": "rw [← Units.eq_iff, LinearEquiv.coe_det, det_rotation, Units.val_one]"
}
] | [
175,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/RingTheory/TensorProduct.lean | LinearMap.baseChange_neg | [
{
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327,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.apply_total_id | [] | [
582,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepFun.mul | [
{
"state_after": "Ω : Type u_1\nι✝ : Type ?u.3504903\nβ✝ : Type ?u.3504906\nβ' : Type ?u.3504909\nγ : Type ?u.3504912\nγ' : Type ?u.3504915\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf✝ : Ω → β✝\ng : Ω → β'\ninst✝² : IsProbabilityMeasure μ\nι : Type u_2\nβ : Type u_3\nm : MeasurableSpace β\ninst✝¹ : ... | [
860,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
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] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.norm_set_integral_le_of_norm_le_const_ae' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.254346\nE : Type u_2\nF : Type ?u.254352\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nC : ℝ\nhs : ↑↑μ s < ⊤\nhC : ∀ᵐ (x : α) ∂μ, x ∈ s → ‖f x‖... | [
538,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/RingQuot.lean | RingQuot.ringQuot_ext' | [
{
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621,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.compl_top | [] | [
387,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iSup_inf_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.2411\ninst✝ : Frame α\ns t : Set α\na✝ b : α\nf : ι → α\na : α\n⊢ (⨆ (i : ι), f i) ⊓ a = ⨆ (i : ι), f i ⊓ a",
"tactic": "rw [iSup, sSup_inf_eq, iSup_range]"
}
] | [
102,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_add | [] | [
786,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.strict_initial | [
{
"state_after": "C : Type u\ninst✝² : Category C\nA B X X' Y Y' Z : C\ninst✝¹ : HasFiniteProducts C\ninst✝ : Exponentiable A\nI : C\nt : IsInitial I\nf : A ⟶ I\nthis : Mono (prod.lift (𝟙 A) f ≫ (zeroMul t).hom)\n⊢ IsIso f",
"state_before": "C : Type u\ninst✝² : Category C\nA B X X' Y Y' Z : C\ninst✝¹ : Ha... | [
378,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.map_map | [] | [
204,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/BoundedOrder.lean | Monotone.forall | [] | [
579,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.convex | [
{
"state_after": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : LinearOrderedRing 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : TopologicalSpace E\ninst✝ : Module 𝕜 E\nA C : Set E\nhA : Convex 𝕜 A\nhAB : IsExposed 𝕜 A ∅\n⊢ Convex 𝕜 ∅\n\ncase inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ ... | [
252,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.isSome_iff | [
{
"state_after": "ι : Type u_1\nI J : Box ι\nx y : ι → ℝ\n⊢ (match ⊥ with\n | some val => true\n | none => false) =\n true ↔\n Set.Nonempty ↑⊥",
"state_before": "ι : Type u_1\nI J : Box ι\nx y : ι → ℝ\n⊢ Option.isSome ⊥ = true ↔ Set.Nonempty ↑⊥",
"tactic": "erw [Option.isSome]"
},
... | [
291,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.tripolar_eq_polar | [] | [
123,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.Anisotropic.eq_zero_iff | [] | [
894,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_clm_comp | [] | [
375,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.im_sum | [] | [
1353,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.sub_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.155050\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : AddCommGroup α\ninst✝ : Neg β\nh : Antiperiodic f c\n⊢ f (c - x) = -f (-x)",
"tactic": "simpa only [sub_eq_neg_add] using h (-x)"
}
] | [
412,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Order/Bounds/Basic.lean | lub_Iio_eq_self_or_Iio_eq_Iic | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns t : Set α\na b : α\ninst✝ : PartialOrder γ\nj i : γ\nhj : IsLUB (Iio i) j\nhj_eq_i : j = i\n⊢ j = i ∨ Iio i = Iic j\n\ncase inr\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preord... | [
563,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_mono' | [
{
"state_after": "α : Type u_1\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f i)) = ∑' (i :... | [
1411,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.548833\nγ : Type ?u.548836\nδ : Type ?u.548839\nι : Type ?u.548842\nR : Type ?u.548845\nR' : Type ?u.548848\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
2679,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2678,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.update | [] | [
1244,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_nonempty_iff | [] | [
219,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.OuterMeasure.le_pi | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.2059615\nα : ι → Type u_1\ninst✝ : Fintype ι\nm✝ m : (i : ι) → OuterMeasure (α i)\nn : OuterMeasure ((i : ι) → α i)\n⊢ (∀ (s : Set ((i : ι) → α i)), Set.Nonempty s → ↑n s ≤ piPremeasure m s) ↔\n ∀ (s : (i : ι) → Set (α i)), Set.Nonempty (Set.pi univ s) → ↑n (Set.p... | [
213,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_eq_zero_of_hasDerivWithinAt' | [
{
"state_after": "case pos\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf f' : ℂ → E\nc : ℂ\nR : ℝ\nh : ∀ (z : ℂ), z ∈ sphere c (Abs.abs R) → HasDerivWithinAt f (f' z) (sphere c (Abs.abs R)) z\nhi : CircleIntegrable f' c R\n⊢ (∮ (z : ℂ) in C(c, R), f' z) = 0\n... | [
480,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Sign.lean | SignType.nonpos_iff | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ a ≤ 0 ↔ a = -1 ∨ a = 0",
"tactic": "cases a <;> decide"
}
] | [
177,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.coe_units_zpow | [
{
"state_after": "no goals",
"state_before": "n' : Type u_2\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_1\ninst✝ : CommRing R\nu : Mˣ\nn : ℕ\n⊢ ↑(u ^ ↑n) = ↑u ^ ↑n",
"tactic": "rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]"
},
{
"state_after": "no goals",
"stat... | [
291,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Std/Data/Int/DivMod.lean | Int.fdiv_nonneg | [] | [
98,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
96,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_set' | [] | [
794,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
792,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.symm | [
{
"state_after": "case H\nε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // ¬p a }\nx : ε\n⊢ ↑(subtypeCongr ep en).symm x = ↑(subtypeCongr ep.symm en.symm) x",
"state_before": "ε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }... | [
598,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | Algebra.lift_algHom_comp_right | [] | [
517,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.sin_eq_sin_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sin x = sin y ↔ ∃ k, y = 2 * ↑k * π + x ∨ y = (2 * ↑k + 1) * π - x",
"tactic": "exact_mod_cast @Complex.sin_eq_sin_iff x y"
}
] | [
226,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_sub_cosh | [] | [
1412,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Data/Set/Basic.lean | Set.setOf_bijective | [] | [
293,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.tr_supports | [
{
"state_after": "Γ : Type u_2\ninst✝³ : Inhabited Γ\nΛ : Type u_1\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nM : Λ → Stmt₁\nencdec : ∀ (a : Γ), dec (enc a) = a\ninst✝ : Fintype Γ\nS : Finset ... | [
1955,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1914,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf g : R\n⊢ zeroLocus {f} ⊆ zeroLocus {g} ↔ g ∈ Ideal.radical (Ideal.span {f})",
"tactic": "rw [← zeroLocus_span {f}, ← zeroLocus_span {g}, zeroLocus_subset_zeroLocus_iff, Ideal.span_le,\n Set.... | [
265,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_of_mul_le_of_one_le_right | [] | [
1094,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq | [] | [
114,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.inv | [] | [
140,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.inv_omega | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | eventually_closedBall_subset | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nX : Type ?u.215446\nι : Type ?u.215449\ninst✝ : PseudoMetricSpace α\nx : α\nu : Set α\nhu : u ∈ 𝓝 x\nε : ℝ\nεpos : 0 < ε\nhε : closedBall x ε ⊆ u\n⊢ ∀ᶠ (r : ℝ) in 𝓝 0, closedBall x r ⊆ u",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.2154... | [
1488,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1484,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_ne_zero | [] | [
75,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.C_mul_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp (↑C a * p) r = ↑C a * comp p r",
"tactic": "induction p using Polynomial.induction_on' with\n| h_add p q hp hq =>\n simp [hp, hq, mul_add]\n| h_monomi... | [
620,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformEmbedding.embedding | [] | [
229,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.tendsto_iff_forall_compact_tendstoUniformlyOn | [
{
"state_after": "no goals",
"state_before": "α : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nι : Type u₃\np : Filter ι\nF : ι → C(α, β)\n⊢ Tendsto F p (𝓝 f) ↔ ∀ (K : Set α), IsCompact K → TendstoUniformlyOn (fun i a => ↑(F i) a) (↑f) ... | [
388,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
src/lean/Init/SimpLemmas.lean | not_decide_eq_true | [
{
"state_after": "no goals",
"state_before": "p : Prop\nh : Decidable p\n⊢ ((!decide p) = true) = ¬p",
"tactic": "cases h <;> simp [decide, *]"
}
] | [
141,
117
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
141,
9
] |
Mathlib/Order/Height.lean | Set.chainHeight_image | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LT α\ninst✝ : LT β\ns✝ t : Set α\nl : List α\na : α\nf : α → β\nhf : ∀ {x y : α}, x < y ↔ f x < f y\ns : Set α\n⊢ ∀ (l : List β), l ∈ subchain (f '' s) → ∃ l', l' ∈ subchain s ∧ length l = length l'\n\ncase a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LT... | [
240,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.toSubMulAction_one | [] | [
108,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.prod_assoc_symm_image | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ✝ : Sort w\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ns : Set α\nt : Set β\nu : Set γ\n⊢ ↑(prodAssoc α β γ).symm '' s ×ˢ t ×ˢ u = (s ×ˢ t) ×ˢ u",
"tactic": "simpa only [Equiv.image_eq_preimage] using prod_assoc_preimage"
}
] | [
162,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_inj | [] | [
173,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ici_succ_of_not_isMax | [] | [
308,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.add_eq_sup | [] | [
419,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.kernel_ι_eq_zero_of_exact_zero_left | [
{
"state_after": "V : Type u\ninst✝³ : Category V\ninst✝² : HasImages V\nA B C D : V\nf : A ⟶ B\ng : B ⟶ C\nh✝ : C ⟶ D\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasEqualizers V\nh : Exact 0 g\n⊢ (kernelSubobjectIso g).inv ≫ Subobject.arrow (kernelSubobject g) = 0",
"state_before": "V : Type u\ninst✝³ : Category... | [
260,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_modifyNth | [] | [
768,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
764,
1
] |
Mathlib/Data/List/Perm.lean | List.rel_perm | [] | [
383,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.lt_last_iff_coe_castPred | [
{
"state_after": "case inl\nn m : ℕ\n⊢ last (n + 1) < last (n + 1) ↔ ↑(castPred (last (n + 1))) = ↑(last (n + 1))\n\ncase inr\nn m : ℕ\ni : Fin (n + 2)\nH : i < last (n + 1)\n⊢ i < last (n + 1) ↔ ↑(castPred i) = ↑i",
"state_before": "n m : ℕ\ni : Fin (n + 2)\n⊢ i < last (n + 1) ↔ ↑(castPred i) = ↑i",
"t... | [
2484,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2478,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_id | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.reflectsMonomorphisms_of_preserves_of_reflects | [] | [
121,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_ρ_inv | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.add_succ_sub_one | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k n m : ℕ\n⊢ n + succ m - 1 = n + m",
"tactic": "rw [add_succ, succ_sub_one]"
}
] | [
300,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
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