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/GroupTheory/Submonoid/Operations.lean | MonoidHom.submonoidMap_surjective | [
{
"state_after": "case mk.intro.intro\nM : Type u_1\nN : Type u_2\nP : Type ?u.149443\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.149464\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.149488\nmc : MonoidHomClass F M N\nf : M →* N\nM' ... | [
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23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Combinatorics/Configuration.lean | Configuration.ProjectivePlane.card_lines | [] | [
523,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
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Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u\nx : FreeRing α\n⊢ ↑(-x) = -↑x",
"tactic": "rw [castFreeCommRing, map_neg]"
}
] | [
345,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
11
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Mathlib/Algebra/Module/LinearMap.lean | AddMonoidHom.toIntLinearMap_injective | [
{
"state_after": "R : Type ?u.355190\nR₁ : Type ?u.355193\nR₂ : Type ?u.355196\nR₃ : Type ?u.355199\nk : Type ?u.355202\nS : Type ?u.355205\nS₃ : Type ?u.355208\nT : Type ?u.355211\nM : Type u_1\nM₁ : Type ?u.355217\nM₂ : Type u_2\nM₃ : Type ?u.355223\nN₁ : Type ?u.355226\nN₂ : Type ?u.355229\nN₃ : Type ?u.3552... | [
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1
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Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.exists_eq_singleton_or_nontrivial | [] | [
812,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
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Mathlib/Data/Fintype/Basic.lean | Finset.compl_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13578\nγ : Type ?u.13581\ninst✝³ : Fintype α\ns t : Finset α\ninst✝² : DecidableEq α\na : α\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : (x : α) → Decidable ¬p x\n⊢ ∀ (a : α), a ∈ filter p univᶜ ↔ a ∈ filter (fun x => ¬p x) univ",
... | [
241,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_toSubmonoid | [] | [
528,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
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Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_neg_neg | [] | [
142,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.continuousOn | [] | [
149,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
11
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Mathlib/Algebra/Lie/DirectSum.lean | DirectSum.bracket_apply | [] | [
125,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Data/List/Basic.lean | List.map₂Left_eq_zipWith | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.466133\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option β → γ\nas : List α\nx✝ : length [] ≤ length []\n⊢ map₂Left f [] [] = zipWith (fun a b => f a (some b)) [] []",
"tactic": "simp"
},
{
"state_after": "no... | [
4124,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4116,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | DifferentiableAt.arctan | [] | [
201,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilter_isOpen_basic | [] | [
57,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Order/Heyting/Basic.lean | le_compl_iff_disjoint_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.156709\nα : Type u_1\nβ : Type ?u.156715\ninst✝ : HeytingAlgebra α\na b c : α\n⊢ a ≤ bᶜ ↔ Disjoint a b",
"tactic": "rw [← himp_bot, le_himp_iff, disjoint_iff_inf_le]"
}
] | [
820,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.add | [] | [
66,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
8
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_eq_minimalPeriod_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf fa : α → α\nfb : β → β\nx y✝ : α\nm n : ℕ\ng : β → β\ny : β\n⊢ minimalPeriod f x = minimalPeriod g y ↔ ∀ (n : ℕ), IsPeriodicPt f n x ↔ IsPeriodicPt g n y",
"tactic": "simp_rw [isPeriodicPt_iff_minimalPeriod_dvd, dvd_right_iff_eq... | [
412,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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Mathlib/Data/Nat/PartENat.lean | PartENat.dom_of_le_some | [] | [
217,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_map | [] | [
1059,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaUncurry_smul | [] | [
1576,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1572,
1
] |
Mathlib/Data/Real/Basic.lean | Real.iInf_nonneg | [] | [
905,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.destruct_nil | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.mono_iff_injective | [] | [
96,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.continuous_totalSpaceMk | [] | [
961,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.addBottom_head_fst | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝² : DecidableEq K\nΓ : K → Type u_2\nΛ : Type ?u.605156\ninst✝¹ : Inhabited Λ\nσ : Type ?u.605162\ninst✝ : Inhabited σ\nL : ListBlank ((k : K) → Option (Γ k))\n⊢ (ListBlank.head (addBottom L)).fst = true",
"tactic": "rw [addBottom, ListBla... | [
2400,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2399,
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Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.injective | [] | [
187,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
11
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | stronglyMeasurable_derivWithin_Ioi | [
{
"state_after": "F : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\ninst✝¹ : CompleteSpace F\ninst✝ : SecondCountableTopology F\nthis✝¹ : MeasurableSpace F := borel F\nthis✝ : BorelSpace F\n⊢ StronglyMeasurable fun x => derivWithin f (Ioi x) x",
"state_before": "F ... | [
820,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Data/Sigma/Interval.lean | Sigma.card_Icc | [] | [
64,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_source | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_one' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.18790\nβ : Type ?u.18793\nM : Type ?u.18796\nN : Type u_2\nG : Type ?u.18802\nk : Type ?u.18805\nR : Type ?u.18808\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf g : ι → N\ns t : Finset ι\nh : ∀ (i : ι), i ∈ s → f i ≤ 1\n⊢ ∏ i i... | [
155,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_neg | [
{
"state_after": "case refine'_1\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 i : ι\nhi : i < i0\n⊢ toZ i0 i ≤ 0\n\ncase refine'_2\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\... | [
238,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean | Ideal.nonarchimedean | [] | [
92,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_re | [] | [
508,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/CategoryTheory/Linear/LinearFunctor.lean | CategoryTheory.Functor.coe_mapLinearMap | [] | [
68,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.drop_append1' | [] | [
122,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_inv' | [] | [
308,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.zero_apply | [] | [
1822,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1821,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_comm | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a b : Bool), xor a b = xor b a",
"tactic": "decide"
}
] | [
263,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.geom_mean_le_arith_mean4_weighted | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nw₁ w₂ w₃ w₄ p₁ p₂ p₃ p₄ : ℝ\nhw₁ : 0 ≤ w₁\nhw₂ : 0 ≤ w₂\nhw₃ : 0 ≤ w₃\nhw₄ : 0 ≤ w₄\nhp₁ : 0 ≤ p₁\nhp₂ : 0 ≤ p₂\nhp₃ : 0 ≤ p₃\nhp₄ : 0 ≤ p₄\nhw : w₁ + w₂ + w₃ + w₄ = 1\n⊢ ↑({ val := w₁, property := hw₁ } + { val := w₂, property := hw₂ }... | [
240,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_map_measure | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.857469\nδ : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → δ\ng : δ → β\nhg : AEStronglyMeasurable g (Measure.map f μ)\nhf : AEMeasurable f\n⊢ Memℒp g 1 ↔... | [
600,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.distortion_bot | [] | [
709,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.flip_apply | [] | [
799,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.eq_zero_or_one_of_isField | [] | [
1233,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toPartENat_surjective | [] | [
1880,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1879,
1
] |
Mathlib/Order/UpperLower/Basic.lean | not_bddBelow_Iio | [] | [
356,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiable_const_sub_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.569259\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
654,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
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] |
Mathlib/Algebra/Order/Module.lean | eq_of_smul_eq_smul_of_neg_of_le | [
{
"state_after": "k : Type u_2\nM : Type u_1\nN : Type ?u.17203\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhab : -c • a = -c • b\nhc : c < 0\nh : a ≤ b\n⊢ a = b",
"state_before": "k : Type u_2\nM : Type u_1\nN : Type ?u.17203\ninst✝... | [
68,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Init/Set.lean | Set.ext | [] | [
53,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/LiminfLimsup.lean | Monotone.isBoundedUnder_le_comp | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Type ?u.197009\ninst✝³ : Nonempty β\ninst✝² : LinearOrder β\ninst✝¹ : Preorder γ\ninst✝ : NoMaxOrder γ\ng : β → γ\nf : α → β\nl : Filter α\nhg : Monotone g\nhg' : Tendsto g atTop atTop\n⊢ IsBoundedUnder (fun x x_1 => x ≤ x_1) l (g ∘ f) → IsBoundedU... | [
1184,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
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] |
Mathlib/Data/Set/Prod.lean | Set.univ_pi_ite | [
{
"state_after": "case h\nι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.166768\ns✝ s₁ s₂ : Set ι\nt✝ t₁ t₂ : (i : ι) → Set (α i)\ni : ι\ns : Set ι\ninst✝ : DecidablePred fun x => x ∈ s\nt : (i : ι) → Set (α i)\nx✝ : (i : ι) → α i\n⊢ (x✝ ∈ pi univ fun i => if i ∈ s then t i else univ) ↔ x✝ ∈ pi s t",
"stat... | [
874,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.singleton_last | [] | [
602,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_sUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u\nA : α → PSet\ny : PSet\nx✝ : y ∈ ⋃₀ mk α A\na : Type (mk α A)\nc : Type (Func (mk α A) a)\ne : Equiv y (Func (A a) c)\nthis : Func (A a) c ∈ mk (Type (A a)) (Func (A a))\n⊢ Func (A a) c ∈ A (?m.27126 α A y x✝ a c e this)",
"tactic": "rwa [eta] at... | [
493,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.one_def | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_iUnion | [] | [
92,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_nil | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_coe' | [
{
"state_after": "n : Nat\n⊢ -[n+1] = -(↑n + 1)",
"state_before": "n : Nat\n⊢ -[n+1] = -↑n - 1",
"tactic": "rw [Int.sub_eq_add_neg, ← Int.neg_add]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ -[n+1] = -(↑n + 1)",
"tactic": "rfl"
}
] | [
502,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
501,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_multilinearMap_injective | [] | [
168,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/MetricSpace/Kuratowski.lean | KuratowskiEmbedding.embeddingOfSubset_dist_le | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf g : { x // x ∈ lp (fun n => ℝ) ⊤ }\nn✝ : ℕ\nC : ℝ\ninst✝ : MetricSpace α\nx : ℕ → α\na✝ b✝ a b : α\nn : ℕ\n⊢ ‖↑(embeddingOfSubset x a - embeddingOfSubset x b) n‖ ≤ dist a b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf g : { x // x ∈ lp (fun... | [
63,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/CharP/Algebra.lean | IsFractionRing.charP_of_isFractionRing | [] | [
139,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_of_not_ge | [] | [
337,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Computability/Halting.lean | ComputablePred.computable_iff | [
{
"state_after": "case intro.intro\nα : Type u_1\nσ : Type ?u.282635\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α → Bool\nh : Computable f\n⊢ ComputablePred fun a => f a = true",
"state_before": "α : Type u_1\nσ : Type ?u.282635\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\np : α → Prop\n⊢ (∃ f, ... | [
178,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.mk_eq_bot_iff | [] | [
794,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.continuousAt_log_iff | [
{
"state_after": "x y : ℝ\n⊢ ContinuousAt log x → x ≠ 0",
"state_before": "x y : ℝ\n⊢ ContinuousAt log x ↔ x ≠ 0",
"tactic": "refine' ⟨_, continuousAt_log⟩"
},
{
"state_after": "y : ℝ\nh : ContinuousAt log 0\n⊢ False",
"state_before": "x y : ℝ\n⊢ ContinuousAt log x → x ≠ 0",
"tactic": "r... | [
329,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_eq_bot' | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1204225\nR₂ : Type u_3\nR₃ : Type ?u.1204231\nR₄ : Type ?u.1204234\nS : Type ?u.1204237\nK : Type ?u.1204240\nK₂ : Type ?u.1204243\nM : Type u_1\nM' : Type ?u.1204249\nM₁ : Type ?u.1204252\nM₂ : Type u_4\nM₃ : Type ?u.1204258\nM₄ : Typ... | [
1359,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_right_injective | [] | [
191,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_zero | [
{
"state_after": "case a\nR : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\nσ : Type u_3\ninst✝¹ : CanonicallyOrderedAddMonoid M\nw : σ → M\nφ : MvPolynomial σ R\ninst✝ : NoZeroSMulDivisors ℕ M\nhw : ∀ (i : σ), w i ≠ 0\nd : σ →₀ ℕ\n⊢ coeff d (↑(weightedHomogeneousComponent w 0) φ) = coeff d (↑C (coeff 0 φ))"... | [
465,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Std/Logic.lean | Or.imp_left | [] | [
251,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
251,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.splitting_map_eq_id | [
{
"state_after": "case h\nC : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ✝¹ Δ' Δ'' : SimplexCategory\ninst✝ : HasFiniteCoproducts C\nΔ✝ : SimplexCategoryᵒᵖ\nx✝¹ : Discrete (Splitting.IndexSet Δ✝)\nA✝ : Splitting.IndexSet Δ✝\nΔ : SimplexCategory\nx✝ : Discrete (S... | [
247,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_add_right | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.451251\nδ : Type ?u.451254\nr : α → β → Prop\np : γ → δ → Prop\nas : Multiset α\nbs₀ bs₁ : Multiset β\n⊢ (∃ bs₀_1 bs₁_1, Rel (flip r) bs₀ bs₀_1 ∧ Rel (flip r) bs₁ bs₁_1 ∧ as = bs₀_1 + bs₁_1) ↔\n ∃ as₀ as₁, Rel r as₀ bs₀ ∧ Rel r as₁ bs₁ ∧ as = as₀ + as... | [
2762,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2760,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.lt_of_lt_floor | [] | [
223,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.map' | [
{
"state_after": "case inl\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module k V\ninst✝³ : AffineSpace V P\nι : Type u_4\nV₂ : Type u_5\nP₂ : Type u_6\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module k V₂\ninst✝ : AffineSpace V₂ P₂\np : ι → P\nhai : AffineIndependent... | [
389,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.ofFin_toFin | [
{
"state_after": "n : ℕ\nv : Bitvec n\n⊢ Bitvec.ofNat n ↑(toFin v) = v",
"state_before": "n : ℕ\nv : Bitvec n\n⊢ ofFin (toFin v) = v",
"tactic": "dsimp [ofFin]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nv : Bitvec n\n⊢ Bitvec.ofNat n ↑(toFin v) = v",
"tactic": "rw [toFin_va... | [
173,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_le_card_height | [
{
"state_after": "l : Type ?u.223607\nm : Type u_2\nn : Type u_3\no : Type ?u.223616\nR : Type u_1\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : CommRing R\ninst✝ : StrongRankCondition R\nA : Matrix m n R\nthis : Module.Finite R (m → R)\n⊢ rank A ≤ Fintype.card m",
"state_before": "l ... | [
154,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_Ioi | [] | [
2350,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2349,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_eq_iff_coe_eq_or_add_eq_pi | [
{
"state_after": "case mp\nθ ψ : ℝ\n⊢ sin θ = sin ψ → ↑θ = ↑ψ ∨ ↑θ + ↑ψ = ↑π\n\ncase mpr\nθ ψ : ℝ\n⊢ ↑θ = ↑ψ ∨ ↑θ + ↑ψ = ↑π → sin θ = sin ψ",
"state_before": "θ ψ : ℝ\n⊢ sin θ = sin ψ ↔ ↑θ = ↑ψ ∨ ↑θ + ↑ψ = ↑π",
"tactic": "constructor"
},
{
"state_after": "case mp\nθ ψ : ℝ\nHsin : sin θ = sin ψ\n... | [
289,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.mapPair_equifibered | [
{
"state_after": "case mk.left.mk.up.up\nJ : Type v'\ninst✝¹ : Category J\nC : Type u\ninst✝ : Category C\nX Y : C\nF F' : Discrete WalkingPair ⥤ C\nα : F ⟶ F'\n⊢ IsPullback (F.map { down := { down := (_ : { as := WalkingPair.left }.as = { as := WalkingPair.left }.as) } })\n (α.app { as := WalkingPair.left }... | [
157,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_think | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ Computation.destruct (destruct (think s)) = Sum.inr (destruct s)",
"tactic": "simp [destruct, think, Computation.rmap]"
}
] | [
639,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_coe' | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.hasSum_integral_of_dominated_convergence | [
{
"state_after": "ι✝ : Type ?u.17150684\n𝕜 : Type ?u.17150687\nE : Type u_2\nF✝ : Type ?u.17150693\nA : Type ?u.17150696\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\na b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nι : Type u_1\ninst✝ : Countable ι\nF : ι → ℝ → E\nb... | [
1039,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
8
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.symmₗ_linearMapAt | [] | [
264,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.one_mod | [] | [
498,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basisDivisor_self | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\n⊢ basisDivisor x x = 0",
"tactic": "simp only [basisDivisor, sub_self, inv_zero, map_zero, MulZeroClass.zero_mul]"
}
] | [
133,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.lt_coe_iff | [
{
"state_after": "no goals",
"state_before": "x : PartENat\nn : ℕ\n⊢ x < ↑n ↔ ∃ h, Part.get x h < n",
"tactic": "simp only [lt_def, forall_prop_of_true, get_natCast', dom_natCast]"
}
] | [
297,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.HasLines.existsUnique_line | [] | [
121,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.nondegenerate_toMatrix_iff | [] | [
589,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_half_subset | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.44437\nι : Type ?u.44440\ninst✝ : PseudoMetricSpace α\nx y✝ z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ny : α\nh : y ∈ ball x (ε / 2)\n⊢ dist y x ≤ ε / 2",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.44437\nι : Type ?u.44440\ninst✝ : PseudoMetricSpace α\nx... | [
666,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.id_app | [] | [
75,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_univ | [] | [
187,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.smul_of_tower_mem | [] | [
243,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_ne_atBot | [] | [
226,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.toPrenex_isPrenex | [] | [
867,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_add_le | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2325640\nG : Type ?u.2325643\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 g : α → E\nhf : AEStronglyMeasurable f μ\nhg : AEStronglyMeasurable g ... | [
754,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.baseSet_at | [] | [
681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/RingTheory/Localization/Module.lean | Basis.localizationLocalization_repr_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nRₛ : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing Rₛ\ninst✝⁸ : Algebra R Rₛ\nS : Submonoid R\nhT : IsLocalization S Rₛ\nA : Type u_3\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\nAₛ : Type u_5\ninst✝⁵ : CommRing Aₛ\ninst✝⁴ : Algebra A Aₛ\ninst✝³... | [
143,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_eq_of_eq | [] | [
827,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Std/Data/AssocList.lean | Std.AssocList.mapKey_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nδ : Type u_2\nβ : Type u_3\nf : α → δ\nl : AssocList α β\n⊢ toList (mapKey f l) =\n List.map\n (fun x =>\n match x with\n | (a, b) => (f a, b))\n (toList l)",
"tactic": "induction l <;> simp [*]"
}
] | [
87,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
85,
9
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.zero_tprodCoeff | [] | [
150,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.top_map | [] | [
157,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Logic/Basic.lean | or_of_or_of_imp_right | [] | [
342,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Topology/Connected.lean | locallyConnectedSpace_iff_connectedComponentIn_open | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nι : Type ?u.115042\nπ : ι → Type ?u.115047\ninst✝ : TopologicalSpace α\ns t u v : Set α\n⊢ LocallyConnectedSpace α → ∀ (F : Set α), IsOpen F → ∀ (x : α), x ∈ F → IsOpen (connectedComponentIn F x)\n\ncase mpr\nα : Type u\nβ : Type v\nι : Type ?u.115042\nπ : ι → ... | [
1180,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_neg | [] | [
89,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
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