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/Set/Sigma.lean | Set.fst_image_sigma_subset | [] | [
242,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sigmaCongrRight_mul | [] | [
243,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_cof | [
{
"state_after": "case intro\nα : Type ?u.94563\nr : α → α → Prop\na : Ordinal\nf : (b : Ordinal) → b < ord (cof a) → Ordinal\nhf : IsFundamentalSequence a (ord (cof a)) f\n⊢ cof (ord (cof a)) = cof a",
"state_before": "α : Type ?u.94563\nr : α → α → Prop\na : Ordinal\n⊢ cof (ord (cof a)) = cof a",
"tac... | [
653,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.map_iInf | [] | [
176,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.ext | [
{
"state_after": "α : Type u_1\na b : Array α\nh₁ : size a = size b\nh₂ : ∀ (i : Nat) (hi₁ : i < size a) (hi₂ : i < size b), getElem a i hi₁ = getElem b i hi₂\n⊢ a = b",
"state_before": "α : Type u_1\na b : Array α\nh₁ : size a = size b\nh₂ : ∀ (i : Nat) (hi₁ : i < size a) (hi₂ : i < size b), getElem a i hi... | [
599,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
566,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.nndist_eq | [] | [
1356,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1356,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.continuousOn_iUnion' | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.4835\nα : Type ?u.4838\nX : Type u_2\nY : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g✝ : ι → Set X\ng : X → Y\nhf : LocallyFinite f\nhc : ∀ (i : ι) (x : X), x ∈ closure (f i) → ContinuousWithinAt g (f i) x\nx : X\n⊢ ContinuousWithinAt g (⋃ ... | [
104,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_infEdist | [] | [
1646,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1645,
1
] |
Std/Data/List/Lemmas.lean | List.subset_cons_of_subset | [] | [
244,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
243,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.length | [
{
"state_after": "n m : ℕ\n⊢ List.length (range' n (m - n)) = m - n",
"state_before": "n m : ℕ\n⊢ List.length (Ico n m) = m - n",
"tactic": "dsimp [Ico]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ List.length (range' n (m - n)) = m - n",
"tactic": "simp only [length_rang... | [
51,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_coe_ne_zero | [] | [
245,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Int.alternating_sum_range_choose | [
{
"state_after": "case zero\nR : Type ?u.168155\n⊢ ∑ m in range (zero + 1), (-1) ^ m * ↑(Nat.choose zero m) = if zero = 0 then 1 else 0\n\ncase succ\nR : Type ?u.168155\nn✝ : ℕ\n⊢ ∑ m in range (Nat.succ n✝ + 1), (-1) ^ m * ↑(Nat.choose (Nat.succ n✝) m) = if Nat.succ n✝ = 0 then 1 else 0",
"state_before": "R... | [
145,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.op_invAct_op_eq | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_ofSubtype | [] | [
472,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_add | [] | [
53,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_mul | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_Ioc | [] | [
266,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pwFilter_idempotent | [] | [
430,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vsub_right_mem_direction_iff_mem | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\np : P\nhp : p ∈ s\np2 : P\n⊢ (∃ p2_1, p2_1 ∈ s ∧ p2 -ᵥ p = p2_1 -ᵥ p) ↔ p2 ∈ s",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u... | [
339,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/NormedSpace/Star/Mul.lean | op_nnnorm_mul | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\ninst✝⁶ : DenselyNormedField 𝕜\ninst✝⁵ : NonUnitalNormedRing E\ninst✝⁴ : StarRing E\ninst✝³ : CstarRing E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : IsScalarTower 𝕜 E E\ninst✝ : SMulCommClass 𝕜 E E\na : E\n⊢ sSup ((fun x => ‖↑(↑(mul 𝕜 E) a) x‖₊) '' Metric.closedBall 0... | [
46,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum₂_mul_add | [] | [
162,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Multiset/NatAntidiagonal.lean | Multiset.Nat.card_antidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑card (antidiagonal n) = n + 1",
"tactic": "rw [antidiagonal, coe_card, List.Nat.length_antidiagonal]"
}
] | [
46,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasInitialChangeUniverse | [] | [
291,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingCoeff_zero | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_closure_coe_preimage | [
{
"state_after": "case refine'_1\nG : Type u_1\nG' : Type ?u.207006\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.207015\ninst✝ : AddGroup A\nH K : Subgroup G\nk✝ k : Set G\nx✝¹ : { x // x ∈ ↑(closure k) }\nx : G\nhx : x ∈ ↑(closure k)\nx✝ : { val := x, property := hx } ∈ ⊤\ng : G\nhg : g ∈ k\n⊢ { val := g,... | [
1182,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence | [
{
"state_after": "case mp\nC : Type u_3\nD : Type u_4\ninst✝² : Category C\ninst✝¹ : Category D\nF : C ⥤ D\nA B : C\nf : A ⟶ B\ninst✝ : IsEquivalence F\n⊢ StrongEpi (F.map f) → StrongEpi f\n\ncase mpr\nC : Type u_3\nD : Type u_4\ninst✝² : Category C\ninst✝¹ : Category D\nF : C ⥤ D\nA B : C\nf : A ⟶ B\ninst✝ : I... | [
343,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.unop_zsmul | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀ | [] | [
455,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.contDiff_cos | [] | [
612,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Set/Opposite.lean | Set.unop_op | [] | [
60,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_mul_snorm_top | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_4\nG : Type u_3\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np : ℝ≥0∞\nf : α → E\nhf : AEStronglyMeasurable f μ\ng : α → F\nb : E → F → G\nh : ∀ᵐ ... | [
1400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
src/lean/Init/Core.lean | Decidable.of_not_not | [] | [
742,
55
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
741,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.mk'_eq_one_iff_eq | [
{
"state_after": "R : Type ?u.224271\ninst✝¹¹ : CommRing R\nM : Submonoid R\nS : Type ?u.224463\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nP : Type ?u.224700\ninst✝⁸ : CommRing P\nA : Type u_1\ninst✝⁷ : CommRing A\ninst✝⁶ : IsDomain A\nK : Type u_2\nB : Type ?u.224883\ninst✝⁵ : CommRing B\ninst✝⁴ : IsDomain B... | [
194,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_image_right | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Sort ?u.246068\nι' : Sort ?u.246071\nι₂ : Sort ?u.246074\nκ : ι → Sort ?u.246079\nκ₁ : ι → Sort ?u.246084\nκ₂ : ι → Sort ?u.246089\nκ' : ι' → Sort ?u.246094\nf : α → β → γ\ns : Set α\nt : Set β\ny : γ\n⊢ (y ∈ ⋃ (b : β) (_ : b ∈ t), (fun a =... | [
1871,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1867,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.comp_contDiffOn_iff | [
{
"state_after": "no goals",
"state_before": "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... | [
345,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_inv | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pure_smul | [] | [
1019,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image | [] | [
1111,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas | [] | [
942,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_add | [
{
"state_after": "no goals",
"state_before": "r p : ℝ\nhr : 0 ≤ r\nhp : 0 ≤ p\n⊢ ↑(toNNReal (r + p)) = ↑(toNNReal r + toNNReal p)",
"tactic": "simp [hr, hp, add_nonneg]"
}
] | [
657,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_apply₁₁ | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_sum_finset_aux | [
{
"state_after": "R : Type u\nι : Type u'\nn✝ : ℕ\nM : Fin (Nat.succ n✝) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝¹² : Semiring R\ninst✝¹¹ : (i : Fin (Nat.succ n✝)) → AddCommMonoid (M i)\ninst✝¹⁰ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁹ : AddCommMonoid M₂\ninst✝⁸ : AddCommMonoi... | [
641,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.sInf_mem | [] | [
2641,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2639,
1
] |
Mathlib/Computability/Partrec.lean | Computable.const | [] | [
287,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.tendsto_add_haar_inter_smul_zero_of_density_zero_aux2 | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2150092\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
689,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAlt_zero | [] | [
1000,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.domain_nontrivial | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.91218\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.91227\nx✝¹ : NonAssocSemiring α\nx✝ : NonAssocSemiring β\nf : α →+* β\nx y : α\ninst✝ : Nontrivial β\nh : 1 = 0\n⊢ ↑f 1 = 0",
"tactic": "rw [h, map_zero]"
}
] | [
623,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/List/Basic.lean | List.length_lookmap | [
{
"state_after": "case h\nι : Type ?u.346880\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option α\nl : List α\n⊢ ∀ (a b : α), b ∈ f a → () = ()",
"state_before": "ι : Type ?u.346880\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option α\nl : List α\n⊢ ... | [
3344,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3343,
1
] |
Std/Data/Option/Lemmas.lean | Option.liftOrGet_some_some | [] | [
191,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
190,
9
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.quotientQuotientEquivQuotientAux_mk | [] | [
633,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_le | [] | [
68,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_inv_apply_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.77340\nα : Type u_1\nβ : Type ?u.77346\nf g : Perm α\np : α → Prop\nx y z : α\n⊢ SameCycle f (↑f⁻¹ x) y ↔ SameCycle f x y",
"tactic": "rw [← sameCycle_apply_left, apply_inv_self]"
}
] | [
155,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.isBasis_gen | [] | [
222,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
11
] |
Mathlib/Data/Part.lean | Part.ofOption_dom | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.9780\nβ : Type ?u.9783\nγ : Type ?u.9786\nα : Type u_1\n⊢ (↑Option.none).Dom ↔ Option.isSome Option.none = true",
"tactic": "simp [ofOption, none]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.9780\nβ : Type ?u.9783\... | [
340,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_preimage_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.35667\nι : Type ?u.35670\nM : Type u_2\nN : Type ?u.35676\ninst✝¹ : One M\ninst✝ : One N\ns✝ t✝ : Set α\nf✝ g : α → M\na : α\ns : Set α\nf : α → M\nt : Set M\nht : ¬1 ∈ t\n⊢ mulIndicator s f ⁻¹' t = f ⁻¹' t ∩ s",
"tactic": "simp [mu... | [
333,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_prod_mk_left | [] | [
687,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/List/ProdSigma.lean | List.product_cons | [] | [
37,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Sum/Interval.lean | Sum.Ico_inl_inl | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.restrictScalars_injective | [] | [
470,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_mul | [] | [
575,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
11
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.image_sub_lt_mul_sub_of_deriv_lt | [
{
"state_after": "E : Type ?u.405058\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.405154\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nC : (fun x => ℝ) 1\nlt_hf' : ∀ (x : ℝ)... | [
854,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.braid_natural | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ : C\ninst✝ : HasBinaryProducts C\nW X Y Z : C\nf : X ⟶ Y\ng : Z ⟶ W\n⊢ prod.map f g ≫ (prod.braiding Y W).hom = (prod.braiding X Z).hom ≫ prod.map g f",
"tactic": "simp"
}
] | [
1001,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsTerminal.comp_from | [] | [
144,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Sign.lean | SignType.le_one | [] | [
211,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAtFilter_id | [] | [
633,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.fullyFaithfulCancelRight_inv_app | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.coeFn_ofIsClosedGraph | [] | [
494,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.preimage_add_right | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.66499\nE : Type u_2\nF : Type ?u.66505\nβ : Type ?u.66508\ninst✝⁵ : OrderedSemiring 𝕜\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace F\ninst✝² : AddCancelCommMonoid E\ninst✝¹ : ContinuousAdd E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : StrictConvex 𝕜 s\nz x : ... | [
228,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_zero | [] | [
82,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma_cong_eq_self | [
{
"state_after": "no goals",
"state_before": "N✝ N : ℕ\ng : ConjAct SL(2, ℤ)\n⊢ g • Gamma N = Gamma N",
"tactic": "apply Subgroup.Normal.conjAct (Gamma_normal N)"
}
] | [
242,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_A' | [] | [
131,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasStrictFDerivAt.cexp | [] | [
125,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.setOf_exists | [] | [
277,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.sumCongr_symm | [] | [
320,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_pow | [
{
"state_after": "F : Type ?u.179852\nα : Type u_1\nβ : Type ?u.179858\nγ : Type ?u.179861\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid α\ns✝ t : Finset α\na : α\nm n✝ : ℕ\ns : Finset α\nn : ℕ\n⊢ ↑(npowRec n s) = ↑s ^ n",
"state_before": "F : Type ?u.179852\nα : Type u_1\nβ : Type ?u.1798... | [
864,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_dropUntil_subset | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nh : u ∈ support p\nx : Dart G\nhx : x ∈ darts (dropUntil p u h)\n⊢ x ∈ darts (takeUntil p u h) ∨ x ∈ darts (dropUntil p u h)",
"state_befo... | [
1154,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.union_mul | [] | [
440,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | pos_of_mul_neg_left | [] | [
1196,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.eq_of_mem_replicate | [] | [
922,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_star | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.819769\nδ : Type ?u.819772\ninst✝⁴ : AddCommMonoid α\ninst✝³ : TopologicalSpace α\ninst✝² : StarAddMonoid α\ninst✝¹ : ContinuousStar α\nf : β → α\na : α\ninst✝ : T2Space α\nhf : Summable f\n⊢ star (∑' (b : β), f b) = ∑' (b : β), star (f b)\n\nc... | [
1427,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.measure_support_lt_top_of_integrable | [] | [
420,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Ioo ↑a ↑b = Ioo a b",
"tactic": "simp [← Ioi_inter_Iio]"
}
] | [
180,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.interior_setOf_le_re | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ interior {z | a ≤ z.re} = {z | a < z.re}",
"tactic": "simpa only [interior_Ici] using interior_preimage_re (Ici a)"
}
] | [
108,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | AlgHom.fieldRange_toSubfield | [] | [
478,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_eq_union_iff_left | [] | [
863,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.sort_sorted_lt | [] | [
92,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_lpPiLpₗᵢ_symm | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_sub_zpow_of_ne | [
{
"state_after": "case inl.intro\nE : Type ?u.690594\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nn : ℤ\nhn✝ : n ≠ -1\nc w : ℂ\nR : ℝ\nhw : w ∈ sphere c (Abs.abs R)\nhn : n < -1\n⊢ (∮ (z : ℂ) in C(c, R), (z - w) ^ n) = 0\n\ncase inr\nE : Type ?u.690594\ninst✝² : NormedAddCo... | [
517,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.dual_comp | [] | [
1498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1496,
1
] |
Mathlib/Data/Part.lean | Part.eq_none_or_eq_some | [] | [
213,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.ClosedComplemented.isClosed | [
{
"state_after": "case intro\nR : Type u_2\ninst✝⁸ : Ring R\nM : Type u_1\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM₂ : Type ?u.2046866\ninst✝⁴ : TopologicalSpace M₂\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : TopologicalAddGroup M\ninst✝ : T1Space M\np : Submodu... | [
2579,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2575,
11
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodUnique_apply | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_preimage_mem_nhds | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.223809\nM' : Type ?u.223812\nH' : Type ?u.223815\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nf f' : LocalHomeomor... | [
1228,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.tendstoLocallyUniformly_iff | [] | [
639,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_comp_lTensor | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1277698\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1277704\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_4\nP : Type u_3\nQ : Type u_5\nS : Type ?u.1277722\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ni... | [
1125,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAtFilter.isBigO_sub | [] | [
426,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsRegular.and_of_mul_of_mul | [] | [
182,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.zero_smul_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.74296\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.74305\ninst✝² : Zero α\ninst✝¹ : Zero β\ninst✝ : SMulWithZero α β\ns : Set α\nt✝ t : Set β\n⊢ 0 • t ⊆ 0",
"tactic": "simp [subset_def, mem_smul]"
}
] | [
798,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Std/Data/Option/Lemmas.lean | Option.get_of_mem | [] | [
28,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
27,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | Metric.bounded_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns : Set α\nt : Set β\n⊢ Bounded (s ×ˢ t) ↔ s = ∅ ∨ t = ∅ ∨ Bounded s ∧ Bounded t",
"tactic": "simp only [bounded_iff_isBounded, Bornology.isBounded_pro... | [
493,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.