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/Analysis/NormedSpace/MStructure.lean | IsLprojection.mul | [
{
"state_after": "X : Type u_2\ninst✝³ : NormedAddCommGroup X\nM : Type u_1\ninst✝² : Ring M\ninst✝¹ : Module M X\ninst✝ : FaithfulSMul M X\nP Q : M\nh₁ : IsLprojection X P\nh₂ : IsLprojection X Q\n⊢ ∀ (x : X), ‖x‖ = ‖(P * Q) • x‖ + ‖(1 - P * Q) • x‖",
"state_before": "X : Type u_2\ninst✝³ : NormedAddCommGr... | [
165,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_prime | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\n⊢ φ p = p - 1",
"tactic": "rw [← pow_one p, totient_prime_pow hp] <;> simp"
}
] | [
229,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsCospearator.isCodetector | [] | [
453,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.withDensity_le_mul | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.4684926\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
608,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.factorial_mul_factorial_dvd_factorial_add | [
{
"state_after": "i j : ℕ\nthis : i ! * (i + j - i)! ∣ (i + j)!\n⊢ i ! * j ! ∣ (i + j)!\n\ncase this\ni j : ℕ\n⊢ i ! * (i + j - i)! ∣ (i + j)!",
"state_before": "i j : ℕ\n⊢ i ! * j ! ∣ (i + j)!",
"tactic": "suffices : i ! * (i + j - i) ! ∣ (i + j)!"
},
{
"state_after": "case this\ni j : ℕ\n⊢ i !... | [
191,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.add_cases | [
{
"state_after": "q : ℚ\nx y : ℝ\n⊢ ¬x + y ∈ Set.range Rat.cast → ¬x ∈ Set.range Rat.cast ∨ ¬y ∈ Set.range Rat.cast",
"state_before": "q : ℚ\nx y : ℝ\n⊢ Irrational (x + y) → Irrational x ∨ Irrational y",
"tactic": "delta Irrational"
},
{
"state_after": "q : ℚ\nx y : ℝ\n⊢ x ∈ Set.range Rat.cast ∧... | [
209,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_biUnion₀ | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1022236\nδ : Type ?u.1022239\nm : MeasurableSpace α\nμ ν : Measure α\nt : Set β\ns : β → Set α\nht : Set.Countable t\nhm : ∀ (i : β), i ∈ t → NullMeasurableSet (s i)\nhd : Set.Pairwise t (AEDisjoint μ on s)\nf : α → ℝ≥0∞\nthis : Encodable ↑t\n⊢ (∫⁻ (a : ... | [
1200,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
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Mathlib/LinearAlgebra/DirectSum/Finsupp.lean | finsuppTensorFinsupp'_single_tmul_single | [
{
"state_after": "case h.mk\nR : Type u\nM : Type v\nN : Type w\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\nS : Type u_1\ninst✝ : CommRing S\nα : Type u_2\nβ : Type u_3\na : α\nb : β\nr₁ r₂ : S\na' : α\nb' : β\n⊢ ↑(↑(finsuppTensorFinsupp' S α β) ... | [
107,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrable_indicator_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1634475\nE : Type u_2\nF : Type ?u.1634481\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nhs : MeasurableSet s\n⊢ Integrable (indicator s f) ↔ IntegrableOn f s",
"tactic": "simp... | [
263,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_ite | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.44\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Pow M ℕ\nP : Prop\ninst✝ : Decidable P\na : M\nb c : ℕ\n⊢ (a ^ if P then b else c) = if P then a ^ b else a ^ c",
"tactic": "split_ifs ... | [
56,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_map | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Order/LocallyFinite.lean | WithBot.Icc_bot_coe | [] | [
1156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
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Mathlib/RingTheory/GradedAlgebra/Radical.lean | Ideal.IsPrime.homogeneousCore | [
{
"state_after": "case I_ne_top\nι : Type u_2\nσ : Type u_3\nA : Type u_1\ninst✝⁴ : CommRing A\ninst✝³ : LinearOrderedCancelAddCommMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nI : Ideal A\nh : IsPrime I\n⊢ (Ideal.homogeneousCore 𝒜 I).toSubmodule ≠ ⊤\n\ncase... | [
166,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_univ | [] | [
1002,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Topology/QuasiSeparated.lean | isQuasiSeparated_univ | [] | [
66,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.one_ne_top | [] | [
107,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_add | [] | [
246,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.toFun_eq_coe | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Set/Image.lean | Function.Injective.mem_set_image | [] | [
226,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.hasInitial_of_isCoseparating | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\ninst✝² : WellPowered C\ninst✝¹ : HasLimits C\n𝒢 : Set C\ninst✝ : Small ↑𝒢\nh𝒢 : IsCoseparating 𝒢\nthis : HasProductsOfShape (↑𝒢) C\n⊢ HasInitial C",
"state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst... | [
303,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Order/Filter/Archimedean.lean | tendsto_nat_cast_atTop_iff | [] | [
37,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.map_one | [] | [
270,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.spanningCoe_le_of_le | [] | [
611,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_apply_eq | [] | [
541,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_sInf | [] | [
732,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.preimage_subset_source | [] | [
445,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.disjoint_nhdsSet_left | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.16218\nπ : ι → Type ?u.16223\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nl : Filter α\nhs : IsCompact s\nH : ∀ (x : α), x ∈ s → Disjoint (𝓝 x) l\n⊢ Disjoint (𝓝ˢ s) l",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.1621... | [
228,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.measurePreserving_mul_right_inv | [] | [
475,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.pointwise_smul_le_iff₀ | [] | [
552,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.not_empty_toList | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α (n + 1)\n⊢ ¬List.isEmpty (toList v) = true",
"tactic": "simp only [empty_toList_eq_ff, Bool.coe_sort_false, not_false_iff]"
}
] | [
220,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow | [
{
"state_after": "x y z : ℝ\nhx : 0 = x ∨ 0 < x\nhxy : x < y\nhz : 0 < z\n⊢ x ^ z < y ^ z",
"state_before": "x y z : ℝ\nhx : 0 ≤ x\nhxy : x < y\nhz : 0 < z\n⊢ x ^ z < y ^ z",
"tactic": "rw [le_iff_eq_or_lt] at hx"
},
{
"state_after": "case inl\nx y z : ℝ\nhxy : x < y\nhz : 0 < z\nhx : 0 = x\n⊢ x... | [
419,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.ccosh | [] | [
502,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_mem_image_coe | [] | [
1525,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_swap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf✝ : α → β → γ\na✝ : Option α\nb✝ : Option β\nc : Option γ\nf : α → β → γ\na : Option α\nb : Option β\n⊢ map₂ f a b = map₂ (fun a b => f b a) b a",
"tactic": "cases a <;> cases b <;> rfl"
}
] | [
90,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\n⊢ (f + g) ≫ h = f ≫ h + g ≫ h",
"tactic": "rw [add_def, sub_comp, neg_def, sub_comp, zero_comp, add_def, neg_def]"
}
] | [
444,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.IsSheaf.hom_ext | [] | [
242,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.minpoly.irreducible | [] | [
253,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.InfiniteNeg.neg | [] | [
463,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.dvd_count_of_dvd_count_mul | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b : Associates α\nhb : b ≠ 0\np : Associates α\nhp : Irreducible p\nhab : ∀ (d :... | [
1785,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1776,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.mem_left_iff_eq_zero_of_disjoint | [] | [
679,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.IsHomogeneous.prod | [
{
"state_after": "σ : Type u_2\nτ : Type ?u.161634\nR : Type u_3\nS : Type ?u.161640\ninst✝ : CommSemiring R\nφ✝ ψ : MvPolynomial σ R\nm n✝ : ℕ\nι : Type u_1\ns : Finset ι\nφ : ι → MvPolynomial σ R\nn : ι → ℕ\n⊢ (∀ (i : ι), i ∈ s → IsHomogeneous (φ i) (n i)) → IsHomogeneous (∏ i in s, φ i) (∑ i in s, n i)",
... | [
205,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.ext | [] | [
113,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | eq_one_of_mul_le_one_right | [] | [
1180,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.has_good_supp_iff | [
{
"state_after": "case mp\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nx : F α\n⊢ (∀ (p : α → Prop), Liftp p x ↔ ∀ (u : α), u ∈ supp x → p u) →\n ∃ a f,\n abs { fst := a, snd := f } = x ∧\n ∀ (a' : (P F).A) (f' : PFunctor.B (P F) a' → α), abs { fst := a', snd := f' } = x → f ''... | [
655,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_iff_not_ge | [] | [
368,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pos_right | [] | [
613,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | FiniteDimensional.nonempty_continuousLinearEquiv_of_finrank_eq | [] | [
417,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_eq_bot_iff_of_injective | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.556305\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.556314\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nH : Subgroup G\nf : G →* N\nhf : Injective ↑f\n⊢ map f H = ⊥ ↔ H = ⊥",
"tactic": "rw [map_eq_bot_iff, f.ker_eq_bot... | [
2964,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2963,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLEMk_comp_ofMkLE | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nB A : C\nX : Subobject B\nf : A ⟶ B\ninst✝ : Mono f\nY : Subobject B\nh₁ : X ≤ mk f\nh₂ : mk f ≤ Y\n⊢ underlying.map (LE.le.hom h₁ ≫ LE.le.hom h₂) = underlying.map (LE.le.hom (_ : X ≤ Y))",
"state_before": "C ... | [
406,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Algebra/MonoidAlgebra/Support.lean | AddMonoidAlgebra.support_single_mul | [] | [
137,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_one | [] | [
205,
30
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204,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_sum | [
{
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.differentiable_set_subset_d | [
{
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223,
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Mathlib/Order/WithBot.lean | WithTop.le_toDual_iff | [] | [
803,
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Mathlib/Combinatorics/Additive/RuzsaCovering.lean | Finset.exists_subset_mul_div | [
{
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.not | [
{
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482,
49
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478,
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Mathlib/Topology/Order.lean | eq_of_nhds_eq_nhds | [] | [
311,
43
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set_union | [] | [
508,
13
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506,
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Mathlib/Topology/Basic.lean | ClusterPt.map | [] | [
1618,
45
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1616,
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Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_eq_sub_sum | [
{
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] | [
160,
19
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156,
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Mathlib/Topology/Sequences.lean | IsSeqCompact.exists_tendsto_of_frequently_mem | [] | [
331,
76
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328,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.desc_comp_assoc | [
{
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] | [
835,
73
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833,
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Mathlib/LinearAlgebra/Isomorphisms.lean | Submodule.card_quotient_mul_card_quotient | [
{
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191,
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.comp_measurable | [] | [
166,
39
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164,
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Mathlib/Logic/Basic.lean | exists_or_eq_right | [] | [
793,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
9
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Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.transferNatTransSelf_adjunction_id | [
{
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31
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208,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_nonempty | [] | [
263,
41
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262,
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Mathlib/Data/SetLike/Basic.lean | SetLike.forall | [] | [
133,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
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Mathlib/LinearAlgebra/Basis.lean | Basis.sumCoords_reindex | [
{
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454,
68
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451,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y = 0\n⊢ ‖x‖ ^ 2 - 2 * (‖x‖ * ‖y‖) + ‖y‖ ^ 2 = (‖x‖ - ‖y‖) ^ 2",
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292,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
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Mathlib/Data/Fin/Basic.lean | Fin.subNat_mk | [] | [
1586,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
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Mathlib/Data/List/Basic.lean | List.indexOf_le_length | [
{
"state_after": "case nil\nι : Type ?u.80422\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na : α\n⊢ indexOf a [] ≤ length []\n\ncase cons\nι : Type ?u.80422\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\nih ... | [
1204,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1198,
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.addSubgroup_independent | [] | [
434,
77
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432,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_sub | [] | [
259,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.generalizedEigenspace_le_generalizedEigenspace_finrank | [] | [
375,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
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Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_add | [] | [
350,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
11
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Mathlib/Algebra/Order/UpperLower.lean | upperClosure_mul_distrib | [
{
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"tactic": "rw [UpperSet.coe_mul, mul_upperClosure, upperClosure_mul, UpperSet.upperClosure]"
}
] | [
320,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.groupSmul_apply | [] | [
1232,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
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Mathlib/Algebra/Support.lean | Function.mulSupport_one_sub' | [
{
"state_after": "no goals",
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434,
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433,
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Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.isUpperSet' | [
{
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133,
101
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125,
1
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.inverse_counitInv_comp | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ ... | [
212,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Std/Data/List/Lemmas.lean | List.chain_cons | [
{
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"tactic": "cases p with | cons n p => exact ⟨n, p⟩"
},
{
"state_after": "no goals",
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1778,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1776,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycleOn_swap | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1649642\nα : Type u_1... | [
802,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.withConstants_relMap_sum_inl | [] | [
518,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_le_of_le | [] | [
2367,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2366,
1
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_transpose_apply | [
{
"state_after": "no goals",
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"tactic": "rw [cramer_apply, upda... | [
107,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_mul_prod_inv | [
{
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156,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Topology/Basic.lean | DenseRange.dense_image | [] | [
1827,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1825,
1
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Mathlib/Order/Antichain.lean | IsStrongAntichain.eq | [] | [
295,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_mul_left | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\nb c : α\n⊢ lcm (0 * b) (0 * c) = ↑normalize 0 * lcm b c",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\na b c : α\n⊢ a = 0 → lcm (a * b) (a * c) = ↑normali... | [
830,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.Bounded.thickening | [
{
"state_after": "case inl\nι : Sort ?u.97539\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\nδ✝ : ℝ\ns : Set α\nx : α\nX : Type u\ninst✝ : PseudoMetricSpace X\nδ : ℝ\nh : Bounded ∅\n⊢ Bounded (thickening δ ∅)\n\ncase inr.intro\nι : Sort ?u.97539\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\nδ... | [
1009,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
11
] |
Mathlib/Algebra/Regular/Basic.lean | not_isRegular_zero | [] | [
269,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_iff_le_and_lf | [] | [
536,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.mul_apply | [] | [
926,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.iSup_coe_eq_top | [
{
"state_after": "α✝ : Type ?u.130874\nβ : Type ?u.130877\nγ : Type ?u.130880\nι✝ : Sort ?u.130883\nι : Sort u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\nf : ι → α\n⊢ (∀ (b : WithTop α), b < ⊤ → ∃ i, b < ↑(f i)) ↔ ∀ (x : α), ∃ y, y ∈ range f ∧ x < y",
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1541,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1534,
1
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Mathlib/Analysis/MeanInequalitiesPow.lean | ENNReal.rpow_add_rpow_le | [
{
"state_after": "ι : Type u\ns : Finset ι\np q : ℝ\na b : ℝ≥0∞\nhp_pos : 0 < p\nhpq : p ≤ q\nh_rpow : ∀ (a : ℝ≥0∞), a ^ q = (a ^ p) ^ (q / p)\n⊢ (a ^ q + b ^ q) ^ (1 / q) ≤ (a ^ p + b ^ p) ^ (1 / p)",
"state_before": "ι : Type u\ns : Finset ι\np q : ℝ\na b : ℝ≥0∞\nhp_pos : 0 < p\nhpq : p ≤ q\n⊢ (a ^ q + b ... | [
338,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_le | [] | [
817,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Order/WithBot.lean | WithBot.wellFounded_lt | [] | [
510,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_orderMonoidWithZeroHom_apply | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.add | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.147588\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nT S : E →L[𝕜] E\nhT : IsPositive T\nhS : IsPo... | [
91,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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