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/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_div_prod | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulRightInvariant μ\n⊢ MeasurePreserving ?m.559954",
"tacti... | [
417,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Topology/Separation.lean | t0Space_iff_nhds_injective | [] | [
214,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Order/Basic.lean | dense_or_discrete | [] | [
1334,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
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Mathlib/GroupTheory/Submonoid/Membership.lean | SubmonoidClass.coe_list_prod | [] | [
52,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.Prepartition.distortion_biUnionTagged | [] | [
436,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
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Mathlib/Computability/Halting.lean | Partrec.merge | [
{
"state_after": "α : Type u_1\nβ : Type ?u.258088\nγ : Type ?u.258091\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf g : α →. σ\nhf : Partrec f\nhg : Partrec g\nH : ∀ (a : α) (x : σ), x ∈ f a → ∀ (y : σ), y ∈ g a → x = y\nk : α →. σ\nhk : Partrec... | [
116,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/Analysis/Complex/Basic.lean | Complex.continuous_ofReal | [] | [
388,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.coe_mk | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.ext_iff | [
{
"state_after": "case mk\nα : Type u_1\nα₁ : Type ?u.3081\nα₂ : Type ?u.3084\nβ : α → Type u_2\nβ₁ : α₁ → Type ?u.3094\nβ₂ : α₂ → Type ?u.3099\nx₁ : Sigma β\nfst✝ : α\nsnd✝ : β fst✝\n⊢ { fst := fst✝, snd := snd✝ } = x₁ ↔\n { fst := fst✝, snd := snd✝ }.fst = x₁.fst ∧ HEq { fst := fst✝, snd := snd✝ }.snd x₁.s... | [
75,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_insert_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.92797\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidableEq α\nh : a ≤ b\n⊢ insert b (Ico a b) = Icc a b",
"tactic": "rw [← coe_inj, coe_insert, coe_Icc, coe_Ico, Set.insert_eq, Set.union_comm, Set.... | [
566,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | card_rootsOfUnity | [] | [
251,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.inf_toSubfield | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_filter_filter_neg | [] | [
2789,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2786,
1
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Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.subset_interior_succ | [] | [
1451,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
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Mathlib/RingTheory/Noetherian.lean | isNoetherian_def | [] | [
89,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_surjective | [
{
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"tactic": "simp [h]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : DecidableEq α\nins... | [
632,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.map_write | [
{
"state_after": "case mk\nΓ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nb head✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ map f (write b { head := head✝, left := left✝, right := right✝ }) =\n write (PointedMap.f f b) (map f { head := head✝, left := left✝, right := ri... | [
698,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
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Mathlib/Data/Finset/Basic.lean | Finset.ssubset_of_ssubset_of_subset | [] | [
433,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/TietzeExtension.lean | BoundedContinuousFunction.exists_forall_mem_restrict_eq_of_closed | [
{
"state_after": "case intro.intro\nX : Type ?u.107579\nY : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : NormalSpace Y\ns : Set Y\nf : ↑s →ᵇ ℝ\nhs : IsClosed s\nt : Set ℝ\ninst✝ : OrdConnected t\nhf : ∀ (x : ↑s), ↑f x ∈ t\nhne : Set.Nonempty t\ng : Y →ᵇ ℝ\nhg : ∀ (y : Y), ↑g y ∈ ... | [
339,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/Module/DedekindDomain.lean | Submodule.isInternal_prime_power_torsion | [
{
"state_after": "R : Type u\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : IsDedekindDomain R\ninst✝ : Module.Finite R M\nhM : Module.IsTorsion R M\nhM' : Module.IsTorsionBySet R M ↑(annihilator ⊤)\n⊢ DirectSum.IsInternal fun p => torsionBySet R M ... | [
77,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ioc_eq_Ioi_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ : α\nf : ι → α\na : α\n⊢ (⋃ (i : ι), Ioc a (f i)) = Ioi a ↔ ∀ (x : α), a < x → ∃ i, x ≤ f i",
"tactic": "simp [← Ioi_inter_Iic, ← inter_iUnion, subset_def]"
}
] | [
162,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.nsmul_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.48063\nγ : Type ?u.48066\ns : Multiset α\nn : ℕ\na : α\n⊢ n • (a ::ₘ s) = n • {a} + n • s",
"tactic": "rw [← singleton_add, nsmul_add]"
}
] | [
705,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | geom_series_mul_neg | [
{
"state_after": "α : Type ?u.1244932\nβ : Type ?u.1244935\nι : Type ?u.1244938\nR : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : R\nh : ‖x‖ < 1\nthis : HasSum (fun i => x ^ i * (1 - x)) ((∑' (b : ℕ), x ^ b) * (1 - x))\n⊢ (∑' (i : ℕ), x ^ i) * (1 - x) = 1",
"state_before": "α : Type ?u.1244... | [
489,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.bot_subgroupOf | [] | [
1639,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_congr_set | [] | [
792,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.coe_fn_injective | [] | [
286,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulSupport_mulIndicator_subset | [] | [
172,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_eq_empty | [] | [
3182,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3181,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.eq_of_eqOn_sdense | [] | [
919,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Order/Basic.lean | update_le_iff | [] | [
867,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.xgcdAux_val | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\n⊢ xgcdAux x 1 0 y 0 1 = (gcd x y, xgcd x y)",
"tactic": "rw [xgcd, ← xgcdAux_fst x y 1 0 0 1, Prod.mk.eta]"
}
] | [
207,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.coe_ne_zero | [] | [
88,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Part.lean | Part.some_ne_none | [
{
"state_after": "α : Type u_1\nβ : Type ?u.5463\nγ : Type ?u.5466\nx : α\nh : some x = none\n⊢ False",
"state_before": "α : Type u_1\nβ : Type ?u.5463\nγ : Type ?u.5466\nx : α\n⊢ some x ≠ none",
"tactic": "intro h"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5... | [
196,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | powers_le_nonZeroDivisors_of_noZeroDivisors | [] | [
148,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.map_of | [] | [
327,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.generate_univ | [] | [
539,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | ContinuousLinearMap.coe_equivProdOfSurjectiveOfIsCompl | [] | [
65,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.natAbs_gcd | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.le_arcsin_iff_sin_le | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : x ∈ Icc (-(π / 2)) (π / 2)\nhy : y ∈ Icc (-1) 1\n⊢ x ≤ arcsin y ↔ sin x ≤ y",
"tactic": "rw [← neg_le_neg_iff, ← arcsin_neg,\n arcsin_le_iff_le_sin ⟨neg_le_neg hy.2, neg_le.2 hy.1⟩ ⟨neg_le_neg hx.2, neg_le.2 hx.1⟩, sin_neg,\n neg_le_neg_iff]"... | [
166,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.zero_right | [] | [
56,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.exists_smul_of_dvd_count | [
{
"state_after": "ι : Type ?u.938329\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : DecidableEq α\ns : Multiset α\nk : ℕ\nh : ∀ (a : α), a ∈ s → k ∣ count a s\n⊢ s = k • ∑ a in toFinset s, (count a s / k) • {a}",
"state_before": "ι : Type ?u.938329\nβ : Type u\nα : Typ... | [
2165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2156,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_one | [] | [
261,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.symm_apply_eq | [] | [
875,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_smul_set | [] | [
322,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin | [
{
"state_after": "a b : ℝ\nn : ℕ\n⊢ -cos b - -cos a = cos a - cos b\n\ncase hderiv\na b : ℝ\nn : ℕ\n⊢ (deriv fun x => -cos x) = fun x => sin x\n\ncase hdiff\na b : ℝ\nn : ℕ\n⊢ ∀ (x : ℝ), x ∈ [[a, b]] → DifferentiableAt ℝ (fun x => -cos x) x\n\ncase hcont\na b : ℝ\nn : ℕ\n⊢ ContinuousOn (fun x => sin x) [[a, b]]... | [
506,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_trans_self | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nβ : Sort v\nγ : Sort w\ne : α ≃ β\n⊢ ∀ (x : β), ↑(e.symm.trans e) x = ↑(Equiv.refl β) x",
"tactic": "simp"
}
] | [
350,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
9
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pullbackIsoUnopPushout_hom_inr | [
{
"state_after": "case a\nC : Type u₁\ninst✝³ : Category C\nJ : Type u₂\ninst✝² : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPushout f.op g.op\n⊢ (pushout.inr ≫ (pullbackIsoUnopPushout f g).hom.op).unop = pullback.snd.op.unop",
"state_before": "C : Type u... | [
662,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.map_map_of_aemeasurable | [
{
"state_after": "case h\nι : Type ?u.2309729\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.2309741\nR : Type ?u.2309744\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nf✝ g✝ : α → β\nμ ν : MeasureTheory.Measure α\ng : β → γ\nf : α → β\nhg : A... | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Order/Max.lean | IsMin.mono | [] | [
307,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nn : ℤ\n⊢ ‖x‖ < ↑p ^ n ↔ ‖x‖ ≤ ↑p ^ (n - 1)",
"tactic": "rw [norm_le_pow_iff_norm_lt_pow_add_one, sub_add_cancel]"
}
] | [
568,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.SpecialLinearGroup.coe_GLPos_neg | [] | [
293,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.liftRel_congr | [] | [
1223,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.int_cyclotomic_spec | [
{
"state_after": "case pos\nn : ℕ\nhzero : n = 0\n⊢ map (Int.castRingHom ℂ) (cyclotomic n ℤ) = cyclotomic' n ℂ ∧\n degree (cyclotomic n ℤ) = degree (cyclotomic' n ℂ) ∧ Monic (cyclotomic n ℤ)\n\ncase neg\nn : ℕ\nhzero : ¬n = 0\n⊢ map (Int.castRingHom ℂ) (cyclotomic n ℤ) = cyclotomic' n ℂ ∧\n degree (cyclot... | [
283,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_left_cancel | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.658823\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx y : M\nc : { x // x ∈ S }\nh : ↑(toMap f) (x * ↑c) = ↑(toMap f) (y * ↑c)\n⊢ ↑(toMap f) (↑(?m.689095 h)... | [
693,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_obj_x_dFrom | [
{
"state_after": "case zero\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZeroObject V\nX : V\n⊢ dFrom ((single₀ V).obj X) Nat.zero = 0\n\ncase succ\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZeroObject V\nX : V\nn✝ : ℕ\n⊢ dFrom ((single₀ V).obj X) (Nat... | [
178,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Resp.Equiv.symm | [] | [
575,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
11
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.norm_setToFun_le' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1698879\nG : Type ?u.1698882\n𝕜 : Type ?u.1698885\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ℝ F'\ninst... | [
1711,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_mul | [] | [
199,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.map_snd_prod | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17061\nδ : Type ?u.17064\nι : Sort ?u.17067\ns : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\nf : Filter α\ng : Filter β\ninst✝ : NeBot f\n⊢ map (Prod.snd ∘ fun p => (p.snd, p.fst)) (g ×ˢ f) = g",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : T... | [
278,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbent_iff_nonneg_lt | [] | [
149,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Computability/Reduce.lean | Equiv.Computable.trans | [] | [
221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.eq_singularPart | [
{
"state_after": "α : Type u_1\nβ : Type ?u.39986\nm : MeasurableSpace α\nμ ν s : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\nhs : s ⟂ₘ ν\nhadd : μ = s + withDensity ν f\nthis : HaveLebesgueDecomposition μ ν\n⊢ s = singularPart μ ν",
"state_before": "α : Type u_1\nβ : Type ?u.39986\nm : MeasurableSpace α\nμ... | [
263,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/Order/Basic.lean | not_tendsto_atBot_of_tendsto_nhds | [] | [
1569,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.t2Space | [] | [
294,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
11
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mem_nonZeroDivisors_iff | [] | [
48,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.embDomain_apply | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.193446\nι : Type ?u.193449\nM : Type u_3\nM' : Type ?u.193455\nN : Type ?u.193458\nP : Type ?u.193461\nG : Type ?u.193464\nH : Type ?u.193467\nR : Type ?u.193470\nS : Type ?u.193473\ninst✝¹ : Zero M\ninst✝ : Zero N\nf : α ↪ β\nv : α →₀ M\na : α\n⊢ (if h ... | [
860,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image2_iInter_subset_left | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort u_4\nι' : Sort ?u.250889\nι₂ : Sort ?u.250892\nκ : ι → Sort ?u.250897\nκ₁ : ι → Sort ?u.250902\nκ₂ : ι → Sort ?u.250907\nκ' : ι' → Sort ?u.250912\nf : α → β → γ\ns✝ : Set α\nt✝ : Set β\ns : ι → Set α\nt : Set β\n⊢ ∀ (x : α), (∀ (i : ι), x ∈ s ... | [
1900,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1897,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ssubset_of_subset_of_ssubset | [] | [
422,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
11
] |
Mathlib/Order/Bounds/Basic.lean | Antitone.map_isGreatest | [] | [
1337,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.comp_concaveOn | [] | [
146,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cmp_eq | [
{
"state_after": "α : Type ?u.468735\nm n : Num\nthis : Ordering.casesOn (cmp m n) (↑m < ↑n) (m = n) (↑n < ↑m)\n⊢ cmp m n = Ordering.eq ↔ m = n",
"state_before": "α : Type ?u.468735\nm n : Num\n⊢ cmp m n = Ordering.eq ↔ m = n",
"tactic": "have := cmp_to_nat m n"
},
{
"state_after": "α : Type ?u.... | [
862,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.coe_to_lieModuleHom | [] | [
1018,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.sum_modByMonic_coeff | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommRing R\np q : R[X]\nhq : Monic q\nn : ℕ\nhn : degree q ≤ ↑n\n✝ : Nontrivial R\n⊢ ∑ i : Fin n, ↑(monomial ↑i) (coeff (p %ₘ q) ↑i) = p %ₘ q",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\... | [
472,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Topology/ContinuousOn.lean | eventually_mem_nhdsWithin | [] | [
157,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.not_prime_mul | [
{
"state_after": "no goals",
"state_before": "a b : ℕ\na1 : 1 < a\nb1 : 1 < b\nh : Prime (a * b)\n⊢ a * 1 = a * b",
"tactic": "simpa using (dvd_prime_two_le h a1).1 (dvd_mul_right _ _)"
}
] | [
221,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.trans | [] | [
621,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_singletonMulHom | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.chaar_nonneg | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nK : Compacts G\nthis : chaar K₀ K ∈ (fun K => Icc 0 ↑(index ↑K ↑K₀)) K\n⊢ 0 ≤ chaar K₀ K",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ :... | [
429,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Polynomial/Monomial.lean | Polynomial.ringHom_ext | [
{
"state_after": "R : Type u\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\nS : Type u_1\ninst✝ : Semiring S\nf g : R[X] →+* S\nh₁ : ∀ (a : R), ↑f (↑C a) = ↑g (↑C a)\nh₂ : ↑f X = ↑g X\nf' : AddMonoidAlgebra R ℕ →+* S := RingHom.comp f (RingEquiv.toRingHom (RingEquiv.symm (toFinsuppIso R)))\nhf' : f' = Ri... | [
84,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasDerivAt_cos | [] | [
81,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_image | [
{
"state_after": "α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\nE : Type u_1\ninst✝ : OrderIsoClass E α β\ne : E\ns : Set α\nhs : OrdConnected s\n⊢ OrdConnected (↑(OrderIso.symm ↑e) ⁻¹' s)",
"state_before": "α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preo... | [
207,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Holor.lean | Holor.mul_assoc0 | [
{
"state_after": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ (x ⊗ y ⊗ z) t = cast (_ : Holor α (ds₁ ++ (ds₂ ++ ds₃)) = Holor α (ds₁ ++ ds₂ ++ ds₃)) (x ⊗ (y ⊗ z)) t",
"state_before": "α : Type\nd : ℕ\... | [
204,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_neg | [
{
"state_after": "x y : ℂ\n⊢ (if x = 0 then if y = 0 then 1 else 0 else exp (-(log x * y))) =\n (if x = 0 then if y = 0 then 1 else 0 else exp (log x * y))⁻¹",
"state_before": "x y : ℂ\n⊢ x ^ (-y) = (x ^ y)⁻¹",
"tactic": "simp only [cpow_def, neg_eq_zero, mul_neg]"
},
{
"state_after": "no goa... | [
107,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.invRev_bijective | [] | [
596,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousSubmodule_eq_finsupp_supported | [
{
"state_after": "case h\nσ : Type u_2\nτ : Type ?u.5216\nR : Type u_1\nS : Type ?u.5222\ninst✝ : CommSemiring R\nn : ℕ\nx✝ : MvPolynomial σ R\n⊢ x✝ ∈ homogeneousSubmodule σ R n ↔ x✝ ∈ Finsupp.supported R R {d | ∑ i in d.support, ↑d i = n}",
"state_before": "σ : Type u_2\nτ : Type ?u.5216\nR : Type u_1\nS :... | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Convex/Independent.lean | ConvexIndependent.injective | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nι : Type u_3\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns t : Set E\np : ι → E\nhc : ConvexIndependent 𝕜 p\ni j : ι\nhij : p i = p j\n⊢ p i ∈ ↑(convexHull 𝕜).toOrderHom (p '' {j})",
"state_before": "𝕜 : Type u_1\nE : Type u_2... | [
79,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
11
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_add_eq_max | [
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ a - b + b = max a b",
"tactic": "match a.le_total b with\n| .inl hl => rw [Nat.max_eq_right hl, Nat.sub_eq_zero_iff_le.mpr hl, Nat.zero_add]\n| .inr hr => rw [Nat.max_eq_left hr, Nat.sub_add_cancel hr]"
},
{
"state_after": "no goals",
... | [
405,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
402,
11
] |
Mathlib/Logic/Equiv/Fintype.lean | Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\ne : Perm α\nf : α ↪ β\nb : β\nh : ¬b ∈ Set.range ↑f\n⊢ ↑(viaFintypeEmbedding e f) b = b",
"tactic": "rwa [Equiv.Perm.viaFintypeEmbedding, Equiv.Perm.extendDomain_apply_not_subtype]"
}
] | [
89,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_iff_memℒp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.360278\nG : Type ?u.360281\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α →ₘ[μ] E\n⊢ f ∈ Lp E p ↔ Memℒp (↑f) p... | [
178,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.49808\ninst✝ : PartialOrder α\na b c : α\ns : Set α\nho : Ioo a b ⊆ s\nhc : s ⊆ Icc a b\nha : a ∈ s\nhb : b ∈ s\n⊢ s ∈ {Icc a b, Ico a b, Ioc a b, Ioo a b}\n\ncase neg\nα : Type u_1\nβ : Type ?u.49808\ninst✝ : PartialOrder α\na b c : α\ns : Set α\nho : Ioo a... | [
936,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
] |
Mathlib/Order/CompleteLattice.lean | isGLB_biInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nβ₂ : Type ?u.162828\nγ : Type ?u.162831\nι : Sort ?u.162834\nι' : Sort ?u.162837\nκ : ι → Sort ?u.162842\nκ' : ι' → Sort ?u.162847\ninst✝ : CompleteLattice α\nf✝ g s✝ t : ι → α\na b : α\ns : Set β\nf : β → α\n⊢ IsGLB (f '' s) (⨅ (x : ... | [
1532,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/Data/Set/Image.lean | Set.mem_image_of_mem | [] | [
221,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.limit_ext_iff' | [] | [
181,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.associator_monoidal | [
{
"state_after": "C : Type u₁\ninst✝⁸ : Category C\ninst✝⁷ : MonoidalCategory C\ninst✝⁶ : BraidedCategory C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : MonoidalCategory D\ninst✝³ : BraidedCategory D\nE : Type u₃\ninst✝² : Category E\ninst✝¹ : MonoidalCategory E\ninst✝ : BraidedCategory E\nX₁ X₂ X₃ Y₁ Y₂ Y₃ : C\... | [
696,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2 | [
{
"state_after": "E : Type u_1\nF : Type ?u.830976\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
1057,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/SetTheory/Lists.lean | Lists.of_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Lists' α true\nx✝ : IsList { fst := true, snd := l }\n⊢ ofList (toList { fst := true, snd := l }) = { fst := true, snd := l }",
"tactic": "simp_all [ofList, of']"
}
] | [
255,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_mul | [] | [
70,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | MixedCharZero.reduce_to_p_prime | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : CommRing R\nP : Prop\n⊢ (∀ (p : ℕ), p > 0 → MixedCharZero R p → P) → ∀ (p : ℕ), Nat.Prime p → MixedCharZero R p → P\n\ncase mpr\nR : Type u_1\ninst✝ : CommRing R\nP : Prop\n⊢ (∀ (p : ℕ), Nat.Prime p → MixedCharZero R p → P) → ∀ (p : ℕ), p > 0 → MixedCharZero R p ... | [
109,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.image_coe_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ico a b = Ico ↑a ↑b",
"tactic": "rw [← preimage_coe_Ico, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Subset.trans Ico_subset_Iio_self <| Iio_subset_Iio le_top)]"
}
] | [
116,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.IsSheaf.isSheafFor | [] | [
741,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
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