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/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_map_of_mem | [] | [
458,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.mk_coe | [] | [
785,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.map_sub | [] | [
317,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
11
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.coe_inj | [] | [
179,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.coe_toRelHom | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_le | [] | [
913,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Order/Antichain.lean | IsStrongAntichain.flip | [] | [
309,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
11
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.wellFounded_of_noetherian | [] | [
524,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_d_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.585751\nF : Type ?u.585754\nK : Type ?u.585757\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\nhd : P.d = 0\n⊢ degree (toPoly P) = ⊥",
"tactic": "rw [of_d_eq_zero ha hb hc hd, d... | [
371,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Order/Monotone/Basic.lean | StrictMono.iterate | [] | [
691,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
11
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_filter | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.397803\nγ : Type ?u.397806\ninst✝¹ : DecidableEq α\np : α → Prop\ninst✝ : DecidablePred p\na : α\ns : Multiset α\nh : p a\n⊢ count a (filter p s) = count a s\n\ncase inr\nα : Type u_1\nβ : Type ?u.397803\nγ : Type ?u.397806\ninst✝¹ : DecidableEq α\np : α → P... | [
2502,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2498,
1
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Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.isOpenMap_proj | [] | [
790,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Manifold/ChartedSpace.lean | chart_target_mem_nhds | [] | [
553,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/Data/Int/Cast/Lemmas.lean | AddMonoidHom.ext_int | [] | [
237,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/AlgebraicTopology/DoldKan/Faces.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq | [
{
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140,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.lt_iff | [
{
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979,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_vadd_right_iff | [
{
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317,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_left_injective' | [] | [
83,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.extract_gcd | [
{
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260,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Data/List/Basic.lean | List.getLast?_singleton | [] | [
768,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Std/Data/List/Lemmas.lean | List.cons_subset_cons | [
{
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"state_before": "α : Type u_1\nl₁ l₂ : List α\na : α\ns : l₁ ⊆ l₂\nx✝ : α\n⊢ x✝ ∈ a :: l₁ → x✝ ∈ a :: l₂",
"tactic": "simp only [mem_cons]"
},
{
"state_after": "no goals",
"sta... | [
247,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
246,
1
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Mathlib/Data/Stream/Init.lean | Stream'.unfolds_head_eq | [] | [
414,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_join | [
{
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"tactic": "simp"
},
{
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"state_before": "α : Type u\nβ : Type v\nγ ... | [
1667,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_mono_measure | [
{
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576,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
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Mathlib/Algebra/Order/Group/Abs.lean | abs_eq_abs | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝¹ : AddGroup α\ninst✝ : LinearOrder α\na b : α\nh : abs a = abs b\n⊢ a = b ∨ a = -b\n\ncase refine'_2\nα : Type u_1\ninst✝¹ : AddGroup α\ninst✝ : LinearOrder α\na b : α\nh : a = b ∨ a = -b\n⊢ abs a = abs b",
"state_before": "α : Type u_1\ninst✝¹ : AddGrou... | [
99,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_iSup_of_directed | [
{
"state_after": "R : Type u\nS✝ : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S✝\ninst✝ : Ring T\nι : Sort u_1\nhι : Nonempty ι\nS : ι → Subring R\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : R\n⊢ (x ∈ ⨆ (i : ι), S i) → ∃ i, x ∈ S i",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\ninst✝² : Ri... | [
1151,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Computability/Language.lean | Language.add_self | [] | [
158,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_of_mem_inter_left | [] | [
1575,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.zero_ne_one_iff | [] | [
149,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_self_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nV : Type u_1\nV' : Type ?u.131151\nP : Type ?u.131154\nP' : Type ?u.131157\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTor... | [
221,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutationsAux2_snd_eq | [
{
"state_after": "no goals",
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"tactic": "rw [← permutationsAux2_append, map_permutationsA... | [
124,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.subset_iUnion | [] | [
248,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_continuousAt_iff | [] | [
421,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.163840\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nE : Type ?u.163859\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf✝ g : α → E\nm m0 : MeasurableSpace α\nμ : Measure α\nhm : m ≤ m0\nf : α → ℝ\nhf : ... | [
201,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.sum | [] | [
355,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.exists_max_root | [] | [
612,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10509\nγ : Type ?u.10512\nδ : Type ?u.10515\nδ' : Type ?u.10518\nι : Sort ?u.10521\ns t u : Set α\nm : MeasurableSpace α\np : Prop\n⊢ MeasurableSet {_a | p}",
"tactic": "by_cases p <;> simp [*]"
}
] | [
246,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym_mono | [] | [
214,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Std/Data/List/Basic.lean | List.modifyNthTR_go_eq | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nf : α✝ → α✝\nacc : Array α✝\nn : Nat\n⊢ modifyNthTR.go f [] n acc = acc.data ++ modifyNth f n []",
"tactic": "cases n <;> simp [modifyNthTR.go, modifyNth]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nf : α✝ → α✝... | [
541,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
538,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_mul | [] | [
107,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isSuccLimit_of_noMax | [
{
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"tactic": "simp"
}
] | [
114,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_Ico | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ card (Ico a b) = ↑b - ↑a",
"tactic": "rw [← Nat.card_Ico, ← map_valEmbedding_Ico, card_map]"
}
] | [
85,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_modifyNthTail | [] | [
751,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
747,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsClopen.prod | [] | [
1582,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_zero_eq_constantCoeff | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\n⊢ ↑(MvPowerSeries.coeff R 0) = ↑(constantCoeff R)",
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"tactic": "rw [coeff, Finsupp.single_zero]"
},
{
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1396,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1394,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.range_coe | [
{
"state_after": "α : Type u_1\ns : Set α\n⊢ val '' univ = s",
"state_before": "α : Type u_1\ns : Set α\n⊢ range val = s",
"tactic": "rw [← Set.image_univ]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Set α\n⊢ val '' univ = s",
"tactic": "simp [-Set.image_univ, coe... | [
1393,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_lpPiLpₗᵢ | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsClosed.hausdorffDist_zero_iff_eq | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.88218\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nhs : IsClosed s\nht : IsClosed t\nfin : hausdorffEdist s t ≠ ⊤\n⊢ hausdorffDist s t = 0 ↔ s = t",
"tactic": "simp [← haus... | [
889,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_finite' | [
{
"state_after": "no goals",
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2222,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2219,
1
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Mathlib/Data/Nat/Fib.lean | Nat.fib_pos | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nn_pos : 0 < n\n⊢ 0 < fib 1",
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.inv_rev | [] | [
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Mathlib/Data/Stream/Init.lean | Stream'.inits_tail | [] | [
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.refl_symm | [] | [
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Mathlib/Order/CompleteLattice.lean | iSup_singleton | [
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Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_sub | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.triangle | [
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.dirac_apply | [] | [
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Mathlib/Topology/Connected.lean | Continuous.connectedComponentsLift_continuous | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ioc_of_le | [] | [
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Mathlib/Dynamics/PeriodicPts.lean | Function.Commute.minimalPeriod_of_comp_eq_mul_of_coprime | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_neg | [
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Mathlib/Algebra/Group/Units.lean | IsUnit.unit_spec | [] | [
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Mathlib/Analysis/Convex/Cone/Dual.lean | ConvexCone.innerDualCone_of_innerDualCone_eq_self | [
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Mathlib/Data/Fintype/Basic.lean | Finset.compl_ne_univ_iff_nonempty | [
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Mathlib/Algebra/Star/Prod.lean | Units.embed_product_star | [] | [
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Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_add | [
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.bot_quotient_isMaximal_iff | [
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Mathlib/Order/Hom/Basic.lean | OrderIso.coe_refl | [] | [
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Mathlib/Data/List/Func.lean | List.Func.equiv_refl | [] | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_symm | [] | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_ofReal | [] | [
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Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_zero | [] | [
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Mathlib/Data/Fin/Basic.lean | Fin.predAbove_above | [
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.ext | [
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Mathlib/Data/List/Indexes.lean | List.mapIdx_append_one | [
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Mathlib/Topology/LocalAtTarget.lean | closedEmbedding_iff_closedEmbedding_of_iSup_eq_top | [
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | continuousOn_extChartAt_symm | [] | [
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.map_sub | [] | [
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.not_mem_Iio_self | [] | [
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.ext | [] | [
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_comp_map | [
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | DifferentiableWithinAt.arsinh | [] | [
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.ofIsoColimit_desc | [] | [
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTrivAsLocalEquiv_source | [] | [
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Iic_filter_lt_of_lt_right | [] | [
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Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.coe_mulLeft | [] | [
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Mathlib/Data/Set/Finite.lean | Set.Finite.biUnion | [
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Mathlib/Algebra/GroupPower/Lemmas.lean | one_add_mul_sub_le_pow | [
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Mathlib/GroupTheory/Submonoid/Membership.lean | ofMul_image_powers_eq_multiples_ofMul | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.span_map_snd | [] | [
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_inv_smul | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_finset | [] | [
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTriv_symm_apply | [] | [
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Mathlib/Init/Algebra/Order.lean | not_lt_of_gt | [] | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_sub | [
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Mathlib/RingTheory/MvPolynomial/Tower.lean | MvPolynomial.aeval_map_algebraMap | [
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Mathlib/Analysis/Normed/Group/Basic.lean | tendsto_iff_norm_tendsto_one | [
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Mathlib/Data/Complex/Exponential.lean | Real.sin_sq_le_one | [
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Mathlib/Algebra/Group/Commute.lean | Commute.one_right | [] | [
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.isTopologicalBasis_cylinders | [
{
"state_after": "case h_open\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\n⊢ ∀ (u : Set ((n : ℕ) → E n)), u ∈ {s | ∃ x n, s = cylinder x n} → IsOpen u\n\ncase h_nhds\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), Discr... | [
388,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
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