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/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain'_smul | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type u_1\ninst✝² : Monoid γ\ninst✝¹ : (i : ι) → AddMonoid (β i)\ninst✝ : (i : ι) → DistribMulAction γ (β i)\nh : κ → ι\nh' : ι → κ\nhh' : Function.LeftInverse h' h\nr : γ\nf : Π₀ (i : ι... | [
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70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
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Mathlib/Order/Filter/Lift.lean | Filter.lift'_inf | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.44318\nι : Sort ?u.44321\nf✝ f₁ f₂ : Filter α\nh h₁ h₂ : Set α → Set β\nf g : Filter α\ns : Set α → Set β\nhs : ∀ (t₁ t₂ : Set α), s (t₁ ∩ t₂) = s t₁ ∩ s t₂\n⊢ (⨅ (i : Bool), Filter.lift' (bif i then f else g) s) = ⨅ (b : Bool), bif b then Filter.lift' f... | [
405,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.braiding_leftUnitor | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX : C\n⊢ (β_ X (𝟙_ C)).hom ≫ (λ_ X).hom = (ρ_ X).hom",
"tactic": "rw [← tensor_right_iff, comp_tensor_id, braiding_leftUnitor_aux₂]"
}
] | [
173,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/RingTheory/TensorProduct.lean | LinearMap.baseChange_tmul | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | Antitone.mul_const_of_nonpos | [] | [
438,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.monomial_smul_single | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nI : Ideal R\nS : Type ?u.189821\ninst✝³ : CommSemiring S\ninst✝² : Algebra S R\ninst✝¹ : Module S M\ninst✝ : IsScalarTower S R M\ni : ℕ\nr : R\nj : ℕ\nm : M\n⊢ r • (↑(Finsupp.lmapDomain M R Nat.succ)... | [
143,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Topology/LocalExtr.lean | Filter.EventuallyLE.isLocalMinOn | [] | [
570,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
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Mathlib/Data/Nat/Prime.lean | Nat.pow_minFac | [
{
"state_after": "case inl\nk : ℕ\nhk : k ≠ 0\n⊢ minFac (1 ^ k) = minFac 1\n\ncase inr\nn k : ℕ\nhk : k ≠ 0\nhn : n ≠ 1\n⊢ minFac (n ^ k) = minFac n",
"state_before": "n k : ℕ\nhk : k ≠ 0\n⊢ minFac (n ^ k) = minFac n",
"tactic": "rcases eq_or_ne n 1 with (rfl | hn)"
},
{
"state_after": "case inr... | [
627,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.ofStar | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.814079\nδ : Type ?u.814082\ninst✝³ : AddCommMonoid α\ninst✝² : TopologicalSpace α\ninst✝¹ : StarAddMonoid α\ninst✝ : ContinuousStar α\nf : β → α\na : α\nhf : Summable fun b => Star.star (f b)\n⊢ Summable f",
"tactic": ... | [
1408,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
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Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul | [] | [
61,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.filter_true | [] | [
617,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.ofLeftInverse_eq_ofInjective | [
{
"state_after": "case H.a\nα✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Type u_1\nβ : Type u_2\nf : α → β\nf_inv : Nonempty α → β → α\nhf : ∀ (h : Nonempty α), LeftInverse (f_inv h) f\nx✝ : α\n⊢ ↑(↑(ofLeftInverse f f_inv hf) x✝) = ↑(↑(ofInjective f (_ : Injective f)) x✝)",
"state_before": "α✝ : Sort u\nβ✝ : S... | [
643,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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Mathlib/Algebra/GroupPower/Basic.lean | Commute.self_zpow | [] | [
502,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_ciSup_set | [] | [
1341,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
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Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.coeff_rename_ne_zero | [
{
"state_after": "σ : Type u_1\nτ : Type u_3\nα : Type ?u.963398\nR : Type u_2\nS : Type ?u.963404\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : σ → τ\nφ : MvPolynomial σ R\nd : τ →₀ ℕ\nh : ∀ (u : σ →₀ ℕ), Finsupp.mapDomain f u = d → coeff u φ = 0\n⊢ coeff d (↑(rename f) φ) = 0",
"state_before": "σ ... | [
324,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | Continuous.integrableAt_nhds | [
{
"state_after": "α : Type u_1\nβ : Type ?u.2377407\nE : Type u_2\nF : Type ?u.2377413\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : TopologicalSpace α\ninst✝² : SecondCountableTopologyEither α E\ninst✝¹ : OpensMeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝ : IsLocallyFiniteMeasure... | [
577,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.iSup_Iic | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.148351\nγ : Type ?u.148354\nι : Sort ?u.148357\nκ : ι → Sort ?u.148362\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t : Set α\nx : α\ns : Set α\nx✝ : α\n⊢ x✝ ∈ ↑(⨆ (a : α) (_ : a ∈ s), Iic a) ↔ x✝ ∈ ↑(lowerClosure s)",
"state_before": "α : Type u_1\nβ : ... | [
1350,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
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Mathlib/Computability/TuringMachine.lean | Turing.TM1.step_supports | [
{
"state_after": "Γ : Type u_1\ninst✝¹ : Inhabited Γ\nΛ : Type u_2\nσ : Type u_3\ninst✝ : Inhabited Λ\nM : Λ → Stmt₁\nS : Finset Λ\nss : Supports M S\nl₁ : Λ\nv : σ\nT : Tape Γ\nc' : Cfg₁\nh₁ : c' ∈ step M { l := some l₁, var := v, Tape := T }\nh₂ : SupportsStmt S (M l₁)\n⊢ c'.l ∈ ↑Finset.insertNone S",
"st... | [
1396,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
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] |
Mathlib/FieldTheory/Normal.lean | AlgHom.restrict_liftNormal | [] | [
433,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
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] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.image_Ioc | [] | [
313,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_nhdsWithin_iff | [] | [
657,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_approxOn | [
{
"state_after": "α : Type ?u.604444\nβ : Type u_2\nι : Type ?u.604450\nE : Type u_1\nF : Type ?u.604456\n𝕜 : Type ?u.604459\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\nq : ℝ\np : ℝ≥0∞\ninst✝¹ : BorelSpace E\nf : β → E\nμ : Measure β\nf... | [
171,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.isCompactlyGenerated_of_wellFounded | [
{
"state_after": "ι : Sort ?u.109474\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : ∀ (k : α), IsCompactElement k\n⊢ IsCompactlyGenerated α",
"state_before": "ι : Sort ?u.109474\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : WellFounded fun x x_1 => x > x_1\n⊢ IsCompactlyGenerated α",
... | [
472,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroidWeightsIndicator_def | [] | [
905,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.le_rpow_one_div_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0\nz : ℝ\nhz : 0 < z\n⊢ x ≤ y ^ (1 / z) ↔ x ^ z ≤ y",
"tactic": "rw [← rpow_le_rpow_iff hz, rpow_self_rpow_inv hz.ne']"
}
] | [
161,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.upperClosure | [] | [
1308,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
11
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.isMittagLeffler_of_exists_finite_range | [
{
"state_after": "J : Type u\ninst✝¹ : Category J\nF : J ⥤ Type v\ni j✝ k : J\ns : Set (F.obj i)\ninst✝ : IsCofilteredOrEmpty J\nh : ∀ (j : J), ∃ i f, Set.Finite (range (F.map f))\nj : J\n⊢ ∃ i f, ∀ ⦃k : J⦄ (g : k ⟶ j), range (F.map f) ⊆ range (F.map g)",
"state_before": "J : Type u\ninst✝¹ : Category J\nF ... | [
268,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.isGLB_sInf | [
{
"state_after": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\nS : Set (Subfield K)\nthis : ∀ {s t : Subfield K}, ↑s ≤ ↑t ↔ s ≤ t\n⊢ IsGLB S (sInf S)",
"state_before": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\nS : Se... | [
648,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.mem_iff | [] | [
109,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ENNReal.measurable_of_measurable_nnreal_prod | [] | [
1843,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : CommGroup α\n⊢ 1⁻ = 1",
"tactic": "rw [m_neg_part_def, inv_one, sup_idem]"
}
] | [
173,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_union | [
{
"state_after": "case h\nτ : Type u_2\nα : Type u_3\nβ : Type u_1\nι : Type ?u.33160\ninst✝ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\ny : β\n⊢ y ∈ ω f ϕ (s₁ ∪ s₂) ↔ y ∈ ω f ϕ s₁ ∪ ω f ϕ s₂",
"state_before": "τ : Type u_2\nα : Type u_3\nβ : Type u_1\nι : Type ?u.33160\ninst✝ : Topo... | [
189,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_add_equiv | [] | [
1472,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.mul_of'_divOf | [
{
"state_after": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\na x✝ : G\n⊢ ↑(x * of' k G a /ᵒᶠ a) x✝ = ↑x x✝",
"state_before": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\na : G\n⊢ x * ... | [
121,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.coe_snd | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Set/Intervals/Infinite.lean | Set.Iic_infinite | [] | [
88,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.naturality | [] | [
154,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub_zsmul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIcoMod hp (a - m • p) b = toIcoMod hp a b - m • p",
"tactic": "simp_rw [sub_eq_add_neg, ← neg_smul, toIcoMod_add_zsmul']"
}
] | [
458,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_nonempty | [] | [
293,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | hasDerivWithinAt_neg | [] | [
247,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_pos | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0∞\n⊢ 0 < ↑x ↔ 0 < x",
"tactic": "rw [← coe_ennreal_zero, coe_ennreal_lt_coe_ennreal_iff]"
}
] | [
553,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_anti_mono | [] | [
240,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_zero | [] | [
633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/LinearAlgebra/Ray.lean | ray_eq_iff | [] | [
275,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_le_ceil_sub | [] | [
857,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.div_lt_one_of_lt | [
{
"state_after": "a b : ℝ≥0\nh : a < b\n⊢ b ≠ 0",
"state_before": "a b : ℝ≥0\nh : a < b\n⊢ a / b < 1",
"tactic": "rwa [div_lt_iff, one_mul]"
},
{
"state_after": "no goals",
"state_before": "a b : ℝ≥0\nh : a < b\n⊢ b ≠ 0",
"tactic": "exact ne_of_gt (lt_of_le_of_lt (zero_le _) h)"
}
] | [
882,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ico_add_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n => Ico (a + ↑n) (a + ↑n + 1))",
"tactic": "simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using\n pairwise_disjoint_Ico_add_zsmul a (1 : α)"
}
] | [
246,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.det_smul_adjugate_adjugate | [
{
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523,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.zero | [
{
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] | [
168,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
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Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_inf_principal_iff | [] | [
1607,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_gc | [
{
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843,
22
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830,
1
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Mathlib/Data/List/Basic.lean | List.nthLe_attach | [] | [
4326,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4325,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.lieSpan_mono | [
{
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635,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | closedEmbedding_smul_left | [] | [
535,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
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Mathlib/Logic/Function/Basic.lean | Function.Surjective.exists | [] | [
213,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
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Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.isLocalization_isLocalization_atPrime_isLocalization | [
{
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155,
52
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151,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.restrict' | [] | [
328,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
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Mathlib/Algebra/Order/Floor.lean | Int.gc_coe_floor | [] | [
649,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_sInf | [] | [
698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.map_natDegree_eq_sub | [
{
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282,
18
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276,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.subsingleton_congr | [] | [
218,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.zero_ne_one | [] | [
251,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.SheafOfTypes.Hom.ext' | [] | [
1057,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.coe_sort_true | [
{
"state_after": "no goals",
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}
] | [
121,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.transReflReparamAux_mem_I | [
{
"state_after": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\nt : ↑I\n⊢ (if ↑t ≤ 1 / 2 then 2 * ↑t else 1) ∈ I",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\nt : ↑I\n⊢ transReflReparamAux t ∈ I",
... | [
148,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_of_continuousOn_differentiableOn | [
{
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1060,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
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Mathlib/Data/Finset/Image.lean | Finset.map_inter | [
{
"state_after": "no goals",
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"tactic": "simp only [coe_map, coe_inter, Set.image_inter f.i... | [
219,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_inter_mul_diff | [] | [
1024,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_nat_cast | [] | [
528,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.size_dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : Ordnode α\n⊢ size (dual t) = size t",
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}
] | [
159,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.abs_mul_cos_add_sin_mul_I | [
{
"state_after": "no goals",
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}
] | [
70,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.rightDistributor_hom | [
{
"state_after": "case w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX : C\nf : J → C\nj✝ : J\n⊢ (rightDistributor X f).hom ≫ biproduct.π (fun j => f j ⊗ X) j✝ =\n (∑ j : ... | [
193,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.sumCongr_swap_refl | [
{
"state_after": "case H\nα✝ : Sort ?u.117460\ninst✝² : DecidableEq α✝\nα : Type u_1\nβ : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ni j : α\nx : α ⊕ β\n⊢ ↑(sumCongr (swap i j) (Equiv.refl β)) x = ↑(swap (Sum.inl i) (Sum.inl j)) x",
"state_before": "α✝ : Sort ?u.117460\ninst✝² : DecidableEq α✝... | [
1668,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousAt.continuousOn | [] | [
868,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_mul | [] | [
230,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.one_lt_aleph0 | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ 1 < ℵ₀",
"tactic": "simpa using nat_lt_aleph0 1"
}
] | [
1414,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion | [] | [
265,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_uniformity_of_eq | [] | [
443,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_inl | [] | [
1862,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1862,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁✝ l₂✝ : List α\nr : α → α → Prop\na b : α\nl₁ l₂ : List α\n⊢ Nodup (l₁ ++ l₂) ↔ Nodup l₁ ∧ Nodup l₂ ∧ Disjoint l₁ l₂",
"tactic": "simp only [Nodup, pairwise_append, disjoint_iff_ne]"
}
] | [
219,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_comp_pseudoEpimorphism | [] | [
324,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Computability/Partrec.lean | Computable.vector_get | [] | [
390,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.fderivWithin_integral_of_tendsto_ae | [] | [
895,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Std/Data/Int/DivMod.lean | Int.zero_emod | [
{
"state_after": "no goals",
"state_before": "b : Int\n⊢ 0 % b = 0",
"tactic": "simp [mod_def', emod]"
}
] | [
252,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
252,
9
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.mono_right | [] | [
462,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | ball_inter | [] | [
639,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono | [] | [
1038,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iUnion₂_mul | [] | [
505,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.csInf_mem | [] | [
2790,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2788,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Basic.lean | GeneralizedContinuedFraction.IntFractPair.coe_to_intFractPair | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualEquivDual_apply | [] | [
1085,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/Computability/Language.lean | Language.append_mem_mul | [] | [
121,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_inter_Iic | [] | [
623,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.exists_lt_add_of_not_principal_add | [
{
"state_after": "a : Ordinal\nha : ¬∀ ⦃a_1 b : Ordinal⦄, a_1 < a → b < a → (fun x x_1 => x + x_1) a_1 b < a\n⊢ ∃ b c x x, b + c = a",
"state_before": "a : Ordinal\nha : ¬Principal (fun x x_1 => x + x_1) a\n⊢ ∃ b c x x, b + c = a",
"tactic": "unfold Principal at ha"
},
{
"state_after": "a : Ordi... | [
176,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_diagonal_eq | [
{
"state_after": "l : Type ?u.310307\nm : Type u\nn : Type u'\nα✝ : Type v\ninst✝⁵ : Fintype n\ninst✝⁴ : DecidableEq n\ninst✝³ : CommRing α✝\nA B : Matrix n n α✝\nα : Type u_1\ninst✝² : Semiring α\nv : n → α\ninst✝¹ : Invertible v\ninst✝ : Invertible (diagonal v)\nthis : Invertible (diagonal v) := diagonalInver... | [
529,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | eventually_closure_subset_of_isCompact_absorbing_of_isOpen_of_omegaLimit_subset' | [
{
"state_after": "case intro.intro\nτ : Type u_2\nα : Type u_3\nβ : Type u_1\nι : Type ?u.37681\ninst✝ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\nc : Set β\nhc₁ : IsCompact c\nn : Set β\nhn₁ : IsOpen n\nhn₂ : ω f ϕ s ⊆ n\nv : Set τ\nhv₁ : v ∈ f\nhv₂ : closure (image2 ϕ v s) ⊆ c\n⊢ ∃ u, ... | [
269,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Int/AbsoluteValue.lean | AbsoluteValue.map_units_int_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommRing S\nabv : AbsoluteValue R S\nx : ℤˣ\ny : R\n⊢ ↑abv (x • y) = ↑abv y",
"tactic": "rcases Int.units_eq_one_or x with (rfl | rfl) <;> simp"
}
] | [
43,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.hasDerivAt_tan | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : cos x ≠ 0\n⊢ HasDerivAt tan (↑1 / cos x ^ 2) x",
"tactic": "exact_mod_cast (Complex.hasDerivAt_tan (by exact_mod_cast h)).real_of_complex"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
... | [
36,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.aeval_esymm_eq_multiset_esymm | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nR : Type u_1\nτ : Type ?u.70471\nS : Type u_2\ninst✝⁴ : CommSemiring R\ninst✝³ : CommSemiring S\ninst✝² : Fintype σ\ninst✝¹ : Fintype τ\ninst✝ : Algebra R S\nf : σ → S\nn : ℕ\n⊢ ↑(aeval f) (esymm σ R n) = Multiset.esymm (Multiset.map f univ.val) n"... | [
177,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Commute.ofNat_right | [] | [
87,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
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