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/Int/Bitwise.lean | Int.bit_negSucc | [
{
"state_after": "b : Bool\nn : ℕ\n⊢ (2 * -[n+1] + bif b then 1 else 0) = -[2 * n + bif !b then 1 else 0+1]",
"state_before": "b : Bool\nn : ℕ\n⊢ bit b -[n+1] = -[Nat.bit (!b) n+1]",
"tactic": "rw [bit_val, Nat.bit_val]"
},
{
"state_after": "no goals",
"state_before": "b : Bool\nn : ℕ\n⊢ (2 ... | [
163,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_id | [] | [
463,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Order/BooleanAlgebra.lean | Bool.inf_eq_band | [] | [
795,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.parts_bot | [] | [
497,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.toAddSubsemigroup_closure | [] | [
110,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.assoc_tmul | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_injective | [
{
"state_after": "case zero\ninst✝ : NeZero Nat.zero\n⊢ Injective val\n\ncase succ\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\n⊢ Injective val",
"state_before": "n : ℕ\ninst✝ : NeZero n\n⊢ Injective val",
"tactic": "cases n"
},
{
"state_after": "case succ\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\na b : ... | [
585,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.ext_iff | [] | [
541,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Logic/Relation.lean | Relation.reflexive_reflTransGen | [] | [
545,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1027026\nγ : Type ?u.1027029\nδ : Type ?u.1027032\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nA B : Set α\nhB : MeasurableSet B\nhAB : Disjoint A B\n⊢ (∫⁻ (a : α) in A ∪ B, f a ∂μ) = (∫⁻ (a : α) in A, f a ∂μ) + ∫⁻ (a : α) in ... | [
1229,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
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Mathlib/Data/Vector/Mem.lean | Vector.mem_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nn : ℕ\na a' : α\nb : β\nv : Vector α n\nf : α → β\n⊢ b ∈ toList (map f v) ↔ ∃ a, a ∈ toList v ∧ f a = b",
"tactic": "rw [Vector.toList_map, List.mem_map]"
}
] | [
81,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_empty | [] | [
363,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.isClopen | [] | [
185,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_subset_Ici_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.72950\ninst✝¹ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\ninst✝ : DenselyOrdered α\nh : Ioi b ⊆ Ici a\n⊢ a ≤ b",
"state_before": "α : Type u_1\nβ : Type ?u.72950\ninst✝¹ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\ninst✝ : DenselyOrdered α\n⊢ Ioi b ⊆ Ici a ↔ a ≤ b",
... | [
1181,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_updateRow_single | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1233103\nm : Type ?u.1233106\nn : Type u_1\no : Type ?u.1233112\nm' : o → Type ?u.1233117\nn' : o → Type ?u.1233122\nR : Type ?u.1233125\nS : Type ?u.1233128\nα : Type v\nβ : Type w\nγ : Type ?u.1233135\nM : Matrix m n α\ni✝ : m\nj : n\nb : n → α\nc ... | [
2868,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2866,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy | [] | [
537,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_le_sub_one_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.123144\nα : Type u_1\nβ : Type ?u.123150\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ ⌊a⌋ ≤ z - 1 ↔ a < ↑z",
"tactic": "rw [← floor_lt, le_sub_one_iff]"
}
] | [
668,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_of_one_div_eq_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.27621\nG : Type ?u.27624\ninst✝ : DivisionMonoid α\na b c : α\nh : 1 / a = 1 / b\n⊢ a = b",
"tactic": "rw [← one_div_one_div a, h, one_div_one_div]"
}
] | [
455,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.add_domain | [] | [
471,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.one_succAbove_zero | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\n⊢ ↑(succAbove 1) 0 = 0",
"tactic": "rfl"
}
] | [
2231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2230,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.mk_le_mk | [] | [
98,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.monotone_face | [] | [
413,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_iSup_comap_of_surjective | [] | [
647,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.ofSigmaCofork_ι_app_left | [] | [
657,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.ext_iff_isBounded | [
{
"state_after": "case h_cobounded.a\nι : Type ?u.6300\nα : Type u_1\nβ : Type ?u.6306\nt t' : Bornology α\nh : ∀ (s : Set α), IsBounded s ↔ IsBounded s\ns : Set α\n⊢ s ∈ cobounded α ↔ s ∈ cobounded α",
"state_before": "ι : Type ?u.6300\nα : Type u_1\nβ : Type ?u.6306\nt t' : Bornology α\nh : ∀ (s : Set α),... | [
242,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.sum_rpow_le_of_tendsto | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_3\nl : Filter ι\ninst✝ : NeBot l\n_i : Fact (1 ≤ p)\nhp : p ≠ ⊤\nC : ℝ\nF : ι → { x // x ∈ lp E p }\nhCF : ∀ᶠ (k : ι) in l, ‖F k‖ ≤ C\nf : (a : α) → E a\nhf : Tendsto (id fun i => ↑(F i)) l (𝓝 ... | [
1156,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv | [] | [
661,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_exp_atTop | [
{
"state_after": "α : Type ?u.20985\nx y z : ℝ\nl : Filter α\nA : Tendsto (fun x => x + 1) atTop atTop\n⊢ Tendsto exp atTop atTop",
"state_before": "α : Type ?u.20985\nx y z : ℝ\nl : Filter α\n⊢ Tendsto exp atTop atTop",
"tactic": "have A : Tendsto (fun x : ℝ => x + 1) atTop atTop :=\n tendsto_atTop_ad... | [
180,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.comp_p | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf : Hom P Q\n⊢ f.f ≫ Q.p = f.f",
"tactic": "rw [f.comm, assoc, assoc, Q.idem]"
}
] | [
93,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/Convex/StrictConvexBetween.lean | Wbtw.dist_le_max_dist | [
{
"state_after": "case pos\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : StrictConvexSpace ℝ V\np p₁ p₂ p₃ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhp₁ : p₂ = p₁\n⊢ dist p₂ p ≤ max (dist p₁ p) (dist p₃ p)\n\ncase neg\nV... | [
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35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_const | [
{
"state_after": "no goals",
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200,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Std/Logic.lean | imp_iff_right | [] | [
113,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
113,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.isConj_iff | [
{
"state_after": "ι : Type ?u.3035426\nα : Type u_1\nβ : Type ?u.3035432\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ τ : Perm α\nhσ : IsCycle σ\nhτ : IsCycle τ\nh : IsConj σ τ\n⊢ card (support σ) = card (support τ)",
"state_before": "ι : Type ?u.3035426\nα : Type u_1\nβ : Type ?u.3035432\ninst✝¹ : Decidab... | [
1755,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1743,
1
] |
Mathlib/CategoryTheory/Monoidal/NaturalTransformation.lean | CategoryTheory.MonoidalNatIso.ofComponents.hom_app | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.isClosed_iUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.8039\nα : Type ?u.8042\nX : Type u_2\nY : Type ?u.8048\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g : ι → Set X\nhf : LocallyFinite f\nhc : ∀ (i : ι), IsClosed (f i)\n⊢ IsClosed (⋃ (i : ι), f i)",
"tactic": "simp o... | [
139,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.neg_one_left | [] | [
82,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.card_eq_one | [] | [
504,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_zsmul | [] | [
311,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/Algebra/UniformMulAction.lean | uniformContinuousConstSMul_of_continuousConstSMul | [] | [
70,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Control/Functor/Multivariate.lean | MvFunctor.id_map' | [] | [
115,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.pairwise_disjoint_on_Ioo_pred | [] | [
96,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.isCountablyGenerated_of_seq | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.110343\nγ : Type ?u.110346\nι : Type ?u.110349\nι' : Sort ?u.110352\nx : ℕ → Set α\n⊢ IsCountablyGenerated (⨅ (i : ℕ), 𝓟 (x i))",
"state_before": "α : Type u_1\nβ : Type ?u.110343\nγ : Type ?u.110346\nι : Type ?u.110349\nι' : Sort ?u.110352\nf : Filte... | [
1157,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.eq_zero_of_mono_cokernel | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝¹ : HasCokernel f\ninst✝ : Mono (cokernel.π f)\n⊢ f ≫ cokernel.π f = 0 ≫ cokernel.π f",
"tactic": "simp"
}
] | [
796,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.isLUB | [
{
"state_after": "case pos\nα : Type u_3\nβ : Type ?u.1154773\nγ : Type ?u.1154776\nγ₂ : Type ?u.1154779\nδ : Type u_2\nι✝ : Sort y\ns t u : Set α\ninst✝¹³ : TopologicalSpace α\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : BorelSpace α\ninst✝¹⁰ : TopologicalSpace β\ninst✝⁹ : MeasurableSpace β\ninst✝⁸ : BorelSpace β\n... | [
1128,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.biInter_mem | [] | [
824,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
] |
Std/Data/Int/Lemmas.lean | Int.mul_neg_one | [
{
"state_after": "no goals",
"state_before": "a : Int\n⊢ a * -1 = -a",
"tactic": "rw [Int.mul_neg, Int.mul_one]"
}
] | [
526,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
526,
11
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.isPositive_iff_complex | [
{
"state_after": "𝕜 : Type ?u.285201\nE : Type ?u.285204\nF : Type ?u.285207\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : InnerProductSpace 𝕜 E\ninst✝⁵ : InnerProductSpace 𝕜 F\ninst✝⁴ : CompleteSpace E\ninst✝³ : CompleteSpace F\nE' : Type u_1\ninst✝² : NormedAdd... | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousLinearMap.norm_compContinuousMultilinearMap_le | [] | [
955,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.union_zero_isClosed | [
{
"state_after": "𝕜 : Type u_1\nA : Type u_2\ninst✝⁸ : CommSemiring 𝕜\ninst✝⁷ : TopologicalSpace 𝕜\ninst✝⁶ : ContinuousAdd 𝕜\ninst✝⁵ : ContinuousConstSMul 𝕜 𝕜\ninst✝⁴ : NonUnitalNonAssocSemiring A\ninst✝³ : TopologicalSpace A\ninst✝² : Module 𝕜 A\ninst✝¹ : T2Space 𝕜\ninst✝ : ContinuousMul 𝕜\n⊢ IsClosed... | [
134,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Logic/Basic.lean | not_ball_of_bex_not | [] | [
1083,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | le_hasSum' | [] | [
202,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_le_mul_iff' | [
{
"state_after": "α β : Type u\na b : Cardinal\nthis : ∀ {a : Cardinal}, ℵ₀ ≤ a → a ≠ 0\n⊢ ℵ₀ ≤ a * b ↔ a ≠ 0 ∧ ℵ₀ ≤ b ∨ ℵ₀ ≤ a ∧ b ≠ 0",
"state_before": "α β : Type u\na b : Cardinal\n⊢ ℵ₀ ≤ a * b ↔ a ≠ 0 ∧ ℵ₀ ≤ b ∨ ℵ₀ ≤ a ∧ b ≠ 0",
"tactic": "have : ∀ {a : Cardinal.{u}}, ℵ₀ ≤ a → a ≠ 0 := fun a => ne_... | [
1586,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1583,
1
] |
Mathlib/Data/List/Indexes.lean | List.oldMapIdx_append | [
{
"state_after": "α : Type u\nβ : Type v\nf : ℕ → α → β\nl : List α\ne : α\n⊢ List.oldMapIdx f (l ++ [e]) = List.oldMapIdx f l ++ [f (length l) e]",
"state_before": "α : Type u\nβ : Type v\n⊢ ∀ (f : ℕ → α → β) (l : List α) (e : α), List.oldMapIdx f (l ++ [e]) = List.oldMapIdx f l ++ [f (length l) e]",
"... | [
102,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
11
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_injective | [] | [
138,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_lt_fib_succ | [
{
"state_after": "case intro\nn : ℕ\nhn : 2 ≤ 2 + n\n⊢ fib (2 + n) < fib (2 + n + 1)",
"state_before": "n : ℕ\nhn : 2 ≤ n\n⊢ fib n < fib (n + 1)",
"tactic": "rcases exists_add_of_le hn with ⟨n, rfl⟩"
},
{
"state_after": "case intro\nn : ℕ\nhn : 2 ≤ 2 + n\n⊢ 0 < fib (n + 1)",
"state_before": ... | [
118,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/List/Basic.lean | List.get_map_rev | [] | [
1297,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1296,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_dvd | [
{
"state_after": "case intro.intro\nR : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : x ∣ z\nH2 : y ∣ z\na b : R\nh : a * x + b * y = 1\n⊢ x * y ∣ z",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH : IsCoprime x y\nH1 : x ∣ z\nH2 : y ∣ z\n⊢ x * y ∣ z",
"tactic": "obtain ⟨a, b, h⟩ :=... | [
126,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_of_le | [] | [
66,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/Algebra/Valuation.lean | Valued.hasBasis_nhds_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\n⊢ Filter.HasBasis (𝓝 0) (fun x => True) fun γ => {x | ↑v x < ↑γ}",
"tactic": "simp [Filter.hasBasis_iff, is_topological_valuation]"
}
] | [
122,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Ioo b c = Ioo (b - a) (c - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
406,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_true | [] | [
675,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Std/Control/ForInStep/Lemmas.lean | ForInStep.bindList_nil | [] | [
21,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
9
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_univ | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.91847\nγ : Type ?u.91850\ns t : Set α\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑univ\na✝ : α\n⊢ a✝ ∈ toFinset univ ↔ a✝ ∈ Finset.univ",
"state_before": "α : Type u_1\nβ : Type ?u.91847\nγ : Type ?u.91850\ns t : Set α\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑univ\... | [
743,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.mem_of_max | [
{
"state_after": "case empty\nF : Type ?u.314698\nα : Type u_1\nβ : Type ?u.314704\nγ : Type ?u.314707\nι : Type ?u.314710\nκ : Type ?u.314713\ninst✝ : LinearOrder α\n⊢ ∀ {a : α}, Finset.max ∅ = ↑a → a ∈ ∅\n\ncase insert\nF : Type ?u.314698\nα : Type u_1\nβ : Type ?u.314704\nγ : Type ?u.314707\nι : Type ?u.3147... | [
1207,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_iff_measurable | [] | [
638,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_monomial_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r✝ p : R[X]\nn d : ℕ\nr : R\n⊢ coeff (↑(monomial n) r * p) (d + n) = r * coeff p d",
"tactic": "rw [← C_mul_X_pow_eq_monomial, mul_assoc, coeff_C_mul, X_pow_mul, coeff_mul_X_pow]"
}
] | [
280,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_le | [] | [
133,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Submonoid.FG.map_injective | [
{
"state_after": "case intro\nM : Type u_2\nN : Type ?u.23387\ninst✝² : Monoid M\ninst✝¹ : AddMonoid N\nM' : Type u_1\ninst✝ : Monoid M'\nP : Submonoid M\ne : M →* M'\nhe : Function.Injective ↑e\ns : Finset M'\nhs : closure ↑s = Submonoid.map e P\n⊢ FG P",
"state_before": "M : Type u_2\nN : Type ?u.23387\ni... | [
164,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_mono_right | [
{
"state_after": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : OrderedCommGroup α\nm✝ n✝ : ℤ\na b : α\nha : 1 ≤ a\nm n : ℤ\nh : m ≤ n\n⊢ a ^ (m + (n - m)) = a ^ n",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH... | [
343,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_lower_bound_start | [
{
"state_after": "n : ℕ\na : ℝ\nh : sqrtTwoAddSeries (↑0 / ↑1) n ≤ 2 - (a / 2 ^ (n + 1)) ^ 2\n⊢ a ≤ 2 ^ (n + 1) * sqrt (2 - sqrtTwoAddSeries 0 n)",
"state_before": "n : ℕ\na : ℝ\nh : sqrtTwoAddSeries (↑0 / ↑1) n ≤ 2 - (a / 2 ^ (n + 1)) ^ 2\n⊢ a < π",
"tactic": "refine' lt_of_le_of_lt _ (pi_gt_sqrtTwoAdd... | [
80,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_min | [] | [
76,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_eq_max_neg | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_strict_mono_of_ae_le_of_ae_lt_on | [] | [
949,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Topology/Instances/Nat.lean | Nat.closedBall_eq_Icc | [
{
"state_after": "case inl\nx : ℕ\nr : ℝ\nhr : 0 ≤ r\n⊢ closedBall x r = Icc ⌈↑x - r⌉₊ ⌊↑x + r⌋₊\n\ncase inr\nx : ℕ\nr : ℝ\nhr : r < 0\n⊢ closedBall x r = Icc ⌈↑x - r⌉₊ ⌊↑x + r⌋₊",
"state_before": "x : ℕ\nr : ℝ\n⊢ closedBall x r = Icc ⌈↑x - r⌉₊ ⌊↑x + r⌋₊",
"tactic": "rcases le_or_lt 0 r with (hr | hr)"
... | [
66,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_quot_mk | [] | [
504,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_mul | [
{
"state_after": "no goals",
"state_before": "p q : ℝ\nhp : 0 ≤ p\n⊢ ↑(toNNReal (p * q)) = ↑(toNNReal p * toNNReal q)",
"tactic": "simp [mul_max_of_nonneg, hp]"
}
] | [
704,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitUpper_eq_bot | [
{
"state_after": "ι : Type u_1\nM : Type ?u.13653\nn : ℕ\nI : Box ι\ni✝ : ι\nx✝ : ℝ\ny : ι → ℝ\ni : ι\nx : ℝ\n⊢ (upper I i ≤ max x (lower I i) ∨ ∃ x x_1, upper I x ≤ lower I x) ↔ upper I i ≤ x",
"state_before": "ι : Type u_1\nM : Type ?u.13653\nn : ℕ\nI : Box ι\ni✝ : ι\nx✝ : ℝ\ny : ι → ℝ\ni : ι\nx : ℝ\n⊢ sp... | [
123,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Conformal.lean | InnerProductGeometry.IsConformalMap.preserves_angle | [
{
"state_after": "case intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : InnerProductSpace ℝ F\nu v : E\nc : ℝ\nhc : c ≠ 0\nli : E →ₗᵢ[ℝ] F\n⊢ angle (↑(c • LinearIsometry.toContinuousLinearMap li) u) (↑(c • Linear... | [
33,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj.commute | [] | [
93,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Logic/Basic.lean | not_bex | [] | [
1079,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | LipschitzWith.vsub | [] | [
258,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ∂ ⊤ = ⊥",
"tactic": "rw [boundary, hnot_top, inf_bot_eq]"
}
] | [
66,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.closure_subset_iff | [] | [
450,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.add | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
1204,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.subtypeRestr_def | [] | [
1368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.frequently_map | [] | [
2850,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2847,
1
] |
Mathlib/RingTheory/Nilpotent.lean | isRadical_iff_span_singleton | [
{
"state_after": "R S : Type u\nx y : R\ninst✝ : CommSemiring R\n⊢ (∀ (n : ℕ) (x : R), x ^ n ∈ Ideal.span {y} → x ∈ Ideal.span {y}) ↔ Ideal.IsRadical (Ideal.span {y})",
"state_before": "R S : Type u\nx y : R\ninst✝ : CommSemiring R\n⊢ IsRadical y ↔ Ideal.IsRadical (Ideal.span {y})",
"tactic": "simp_rw [... | [
124,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_eq_of_eq_mul_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.52587\nβ : Type ?u.52590\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a = c * b⁻¹\n⊢ a * b = c",
"tactic": "simp [h]"
}
] | [
663,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Order/CompleteLatticeIntervals.lean | sInf_within_of_ordConnected | [
{
"state_after": "case intro\nα : Type u_1\ns✝ : Set α\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\nhs : OrdConnected s\nt : Set ↑s\nh_bdd : BddBelow t\nc : ↑s\nhct : c ∈ t\n⊢ sInf (Subtype.val '' t) ∈ s",
"state_before": "α : Type u_1\ns✝ : Set α\ninst✝ : ConditionallyCompleteLinearOrder α\ns : ... | [
154,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.eq_σ_of_epi | [
{
"state_after": "case intro.intro\nn : ℕ\nθ : [n + 1] ⟶ [n]\ninst✝ : Epi θ\ni : Fin (n + 1)\nθ' : [n] ⟶ [n]\nh : θ = σ i ≫ θ'\n⊢ ∃ i, θ = σ i",
"state_before": "n : ℕ\nθ : [n + 1] ⟶ [n]\ninst✝ : Epi θ\n⊢ ∃ i, θ = σ i",
"tactic": "rcases eq_σ_comp_of_not_injective θ (by\n by_contra h\n simpa using le_... | [
743,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_zpow_apply_self | [
{
"state_after": "ι : Type ?u.2180524\nα : Type u_1\nβ : Type ?u.2180530\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y : α\nf : Perm α\nx : α\nz : ℤ\n⊢ ↑(cycleOf f x ^ z) x = ↑(f ^ z) x",
"state_before": "ι : Type ?u.2180524\nα : Type u_1\nβ : Type ?u.2180530\ninst✝¹ : DecidableEq α\ninst✝... | [
997,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAntiOn.antitoneOn | [] | [
462,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
11
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.coe_inv | [] | [
215,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_apply_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ninst✝¹ : (i : ι) → Zero (β i)\np : ι → Prop\ninst✝ : DecidablePred p\nf : Π₀ (i : ι), β i\ni : ι\nh : p i\n⊢ ↑(filter p f) i = ↑f i",
"tactic": "simp only [filter_apply, if_pos h]"
... | [
412,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.Γ_map_op | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_singleton_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\n⊢ lookup a (singleton a b) = some b",
"tactic": "rw [singleton, lookup_toFinmap, AList.singleton, AList.lookup, dlookup_cons_eq]"
}
] | [
308,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.iget_map | [
{
"state_after": "P : PFunctor\nα✝ β✝ : Type u\ninst✝² : DecidableEq P.A\nα β : Type u\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\nx : Obj P α\nf : α → β\ni : IdxCat P\nh : i.fst = x.fst\n⊢ Sigma.snd (f <$> x) (cast (_ : B P i.fst = B P (f <$> x).fst) i.snd) =\n f (Sigma.snd x (cast (_ : B P i.fst = B P x.fs... | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.d_comp_eqToHom | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ni j : ι\nrij rij' : ComplexShape.Rel c i j\n⊢ d C i j ≫ eqToHom (_ : X C j = X C j) = d C i j",
"state_before": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ :... | [
322,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_zpow' | [] | [
1303,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
11
] |
Mathlib/Order/Filter/NAry.lean | Filter.NeBot.map₂ | [] | [
134,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
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