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/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.sub | [] | [
331,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
11
] |
Mathlib/Order/CompleteLattice.lean | iInf_subtype' | [] | [
1212,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_div | [] | [
581,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.max_mul | [] | [
993,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.bddAbove | [] | [
1596,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
11
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Ring R\nf g : ℕ → R\n⊢ (∀ (n : ℕ), 0 < n → ∑ x in divisorsAntidiagonal n, ↑μ x.fst • g x.snd = f n) ↔\n ∀ (n : ℕ), 0 < n → ∑ x in divisorsAntidiagonal n, ↑(↑μ x.fst) * g x.snd = f n",
"state_before": "R : Type u_1\ninst✝ : Ring R\nf g : ℕ → R\n⊢ (∀ (n : ℕ), 0 < n →... | [
1131,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_div' | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 ≤ y\n⊢ sqrt (x / y) = sqrt x / sqrt y",
"tactic": "rw [division_def, sqrt_mul' x (inv_nonneg.2 hy), sqrt_inv, division_def]"
}
] | [
416,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/RingTheory/MvPolynomial/Symmetric.lean | MvPolynomial.esymm_eq_multiset_esymm | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\nτ : Type ?u.69783\nS : Type ?u.69786\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S\ninst✝¹ : Fintype σ\ninst✝ : Fintype τ\n⊢ esymm σ R = Multiset.esymm (Multiset.map X univ.val)",
"tactic": "refine' funext fun n => (Finset.esy... | [
172,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/Data/Set/Lattice.lean | Set.inter_iInter_nat_succ | [] | [
2228,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2227,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.isOpen | [
{
"state_after": "α : Type u\nt : TopologicalSpace α\ns : Set α\nb : Set (Set α)\nhb : IsTopologicalBasis b\nhs : s ∈ b\n⊢ IsOpen s",
"state_before": "α : Type u\nt : TopologicalSpace α\ns : Set α\nb : Set (Set α)\nhb : IsTopologicalBasis b\nhs : s ∈ b\n⊢ IsOpen s",
"tactic": "rw [hb.eq_generateFrom]"
... | [
171,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
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Mathlib/GroupTheory/Nilpotent.lean | descending_central_series_ge_lower | [] | [
339,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.sumCongr_trans | [] | [
315,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.codRestrict_apply | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target_aux | [
{
"state_after": "H : Type u_2\nM : Type ?u.20880\nH' : Type u_3\nM' : Type u_4\nX : Type u_1\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : StructureGr... | [
290,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/FieldTheory/IntermediateField.lean | mem_subalgebraEquivIntermediateField | [] | [
758,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.isSymm_compl | [
{
"state_after": "case a.h\nV : Type u_2\nα : Type u_1\nβ : Type ?u.14711\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq V\nA : Matrix V V α\ninst✝¹ : Zero α\ninst✝ : One α\nh : IsSymm A\ni✝ x✝ : V\n⊢ (compl A)ᵀ i✝ x✝ = compl A i✝ x✝",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.14711\ninst✝³ : ... | [
120,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.isConj_swap_mul_swap_of_cycleType_two | [
{
"state_after": "α : Type ?u.175293\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm (Fin 5)\nha : g ∈ alternatingGroup (Fin 5)\nh1 : g ≠ 1\nh2 : ∀ (n : ℕ), n ∈ cycleType g → n = 2\nh : Finset.card (support g) ≤ card (Fin 5)\n⊢ IsConj (swap 0 4 * swap 1 3) g",
"state_before": "α : Type ?u.175293\ninst✝... | [
306,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.of_surjective | [
{
"state_after": "p : ℕ\nG : Type u_2\ninst✝¹ : Group G\nhG : IsPGroup p G\nH : Type u_1\ninst✝ : Group H\nϕ : G →* H\nhϕ : Function.Surjective ↑ϕ\nh : H\ng : G\nhg : ↑ϕ g = h\nk : ℕ\nhk : g ^ p ^ k = 1\n⊢ h ^ p ^ k = 1",
"state_before": "p : ℕ\nG : Type u_2\ninst✝¹ : Group G\nhG : IsPGroup p G\nH : Type u_... | [
90,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_orthonormal' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : IsWellOrder ι fun x x_1 => x < x_1\nf : ι → E\n⊢ ∀ {i j : ↑{i | gramSchmidtNormed 𝕜 f i ≠ 0}},\n ... | [
316,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.fg_def | [] | [
928,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | div_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.19455\nM₀ : Type ?u.19458\nG₀ : Type u_1\nM₀' : Type ?u.19464\nG₀' : Type ?u.19467\nF : Type ?u.19470\nF' : Type ?u.19473\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na b c : G₀\n⊢ a / b = 0 ↔ a = 0 ∨ b = 0",
"tactic": "simp [div_eq_mul... | [
290,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.surjective_iff_surjective_of_iUnion_eq_univ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.186386\nι : Sort ?u.186389\nι' : Sort ?u.186392\nι₂ : Sort ?u.186395\nκ : ι → Sort ?u.186400\nκ₁ : ι → Sort ?u.186405\nκ₂ : ι → Sort ?u.186410\nκ' : ι' → Sort ?u.186415\ns : Set β\nf : α → β\nU : ι → Set β\nhU : iUnion U = univ\nH : ∀ (i : ι), Surjective... | [
1514,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1508,
1
] |
Mathlib/Logic/Basic.lean | Ne.ne_or_ne | [] | [
762,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.ofFinset_apply_of_not_mem | [] | [
178,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.finrank_quotient_map | [
{
"state_after": "R : Type u\ninst✝²⁶ : CommRing R\nS : Type v\ninst✝²⁵ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\ninst✝²⁴ : Algebra R S\nK : Type u_1\ninst✝²³ : Field K\ninst✝²² : Algebra R K\nhRK : IsFractionRing R K\nL : Type u_2\ninst✝²¹ : Field L\ninst✝²⁰ : Algebra S L\ninst✝¹⁹ : IsFractionRing S... | [
448,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.Iso.hom_inv_id_app | [] | [
71,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Sites/CompatibleSheafification.lean | CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app | [
{
"state_after": "C : Type u\ninst✝⁸ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁷ : Category D\nE : Type w₂\ninst✝⁶ : Category E\nF : D ⥤ E\ninst✝⁵ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁴ : ∀ (α β : Type (max v u)) (fst snd : β → α),... | [
126,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_sup | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | one_le_gauge_of_not_mem | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.97683\nE : Type u_1\nF : Type ?u.97689\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\nx : E\nhs₁ : StarConvex ℝ 0 s\nhs₂ : Absorbs ℝ s {x}\nhx : ¬x ∈ s\n⊢ ¬x ∈ 1 • s",
"tactic": "rwa [one_smul]"
}
] | [
238,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.bsup_lt_ord_lift | [] | [
469,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.nnnorm_coe | [] | [
83,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgEquiv.ofLeftInverse_apply | [] | [
712,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_assoc | [] | [
195,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.supp_eq | [
{
"state_after": "case h\nn m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor m\nα✝ β : TypeVec m\nα : TypeVec n\na : P.A\nf : B P a ⟹ α\ni : Fin2 n\nx : α i\n⊢ x ∈ supp { fst := a, snd := f } i ↔ x ∈ f i '' univ",
"state_before": "n m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor m\nα✝ β : TypeVec m\nα : T... | [
216,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.span_image_eq_map_total | [
{
"state_after": "case h₁\nα : Type u_1\nM : Type u_2\nN : Type ?u.379165\nP : Type ?u.379168\nR : Type u_3\nS : Type ?u.379174\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R ... | [
690,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.map_comp | [] | [
96,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_zero | [] | [
355,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_neg_one | [
{
"state_after": "no goals",
"state_before": "n✝ n : ℕ\n⊢ ofDigits (-1) [n] = List.alternatingSum (List.map (fun n => ↑n) [n])",
"tactic": "simp [ofDigits, List.alternatingSum]"
},
{
"state_after": "n a b : ℕ\nt : List ℕ\n⊢ ↑a + -1 * (↑b + -1 * List.alternatingSum (List.map (fun n => ↑n) t)) =\n... | [
575,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_app_left | [] | [
290,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_int_mul_two_pi_sub_pi | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ cos (↑n * (2 * π) - π) = -1",
"tactic": "simpa only [cos_zero] using (cos_periodic.int_mul n).sub_antiperiod_eq cos_antiperiodic"
}
] | [
401,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.nnnorm_star | [] | [
93,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_one | [] | [
1040,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | LocalHomeomorph.hasStrictDerivAt_symm | [] | [
85,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.NeBot.mono | [] | [
505,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.w | [
{
"state_after": "case w\nC : Type u₁\ninst✝³ : Category C\nA : Type u₂\ninst✝² : Category A\nJ : GrothendieckTopology C\nU : C\nR : Presieve U\nP : Cᵒᵖ ⥤ A\ninst✝¹ : HasProducts A\ninst✝ : HasPullbacks C\n⊢ ∀ (j : Discrete (((V : C) × { f // R f }) × (W : C) × { g // R g })),\n (forkMap R P ≫ firstMap R P) ... | [
576,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.lt | [
{
"state_after": "case intro\ny : ℝ*\nr s : ℝ\nhys : IsSt y s\nhrs : r < s\nf : ℕ → ℝ\nhxr : IsSt (ofSeq f) r\n⊢ ofSeq f < y",
"state_before": "x y : ℝ*\nr s : ℝ\nhxr : IsSt x r\nhys : IsSt y s\nhrs : r < s\n⊢ x < y",
"tactic": "rcases ofSeq_surjective x with ⟨f, rfl⟩"
},
{
"state_after": "case ... | [
273,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
11
] |
Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.MonadHom.id_toNatTrans | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_ofMul | [] | [
106,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Std/Data/String/Lemmas.lean | String.contains_iff | [
{
"state_after": "no goals",
"state_before": "s : String\nc : Char\n⊢ contains s c = true ↔ c ∈ s.data",
"tactic": "simp [contains, any_iff]"
}
] | [
728,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
727,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_range | [] | [
1178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.comp_continuousOn | [] | [
348,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Std/Logic.lean | iff_and_self | [
{
"state_after": "no goals",
"state_before": "p q : Prop\n⊢ (p ↔ q ∧ p) ↔ p → q",
"tactic": "rw [and_comm, iff_self_and]"
}
] | [
217,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
217,
9
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousWithinAt_univ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : TopologicalSpace α\nβ : Type u_2\ninst✝ : Preorder β\nf g : α → β\nx : α\ns t : Set α\ny z : β\n⊢ UpperSemicontinuousWithinAt f univ x ↔ UpperSemicontinuousAt f x",
"tactic": "simp [UpperSemicontinuousWithinAt, UpperSemicontinuousAt, n... | [
677,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.support_formPerm_of_nodup' | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.764613\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nh : Nodup l\nh' : ∀ (x : α), l ≠ [x]\n⊢ {x | ↑(formPerm l) x ≠ x} ≤ ↑(toFinset l)\n\ncase a\nα : Type u_1\nβ : Type ?u.764613\ninst✝ : DecidableEq α\nl✝ : List α\nx : α\nl : List α\nh : Nodup l\nh'... | [
262,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_eq_image_lineMap | [
{
"state_after": "case h.e'_3.h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.88569\nG : Type ?u.88572\nι : Type ?u.88575\nπ : ι → Type ?u.88580\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\na✝¹ : 𝕜\na✝ : a✝¹... | [
227,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimits.hasColimitsOfShape | [] | [
682,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_left | [] | [
41,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
41,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.Nonempty.sigma_snd | [] | [
215,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/CharP/Basic.lean | add_pow_char_pow | [] | [
282,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_empty_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u t s : Set α\n⊢ Set.ite t s ∅ = s ∩ t",
"tactic": "simp [Set.ite]"
}
] | [
2291,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2291,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.tail_neg | [] | [
593,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_zero | [
{
"state_after": "case h\nR₁ : Type u_6\nR₂ : Type u_1\nR₃ : Type u_2\ninst✝¹⁷ : Semiring R₁\ninst✝¹⁶ : Semiring R₂\ninst✝¹⁵ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_5\ninst✝¹⁴ : TopologicalSpace M₁\ninst✝¹³ : AddCommMonoid M₁\nM'₁ : Type ?u.510286\ninst✝¹² : TopologicalSpac... | [
808,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Module.lean | ContinuousLinearEquiv.summable | [] | [
85,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
11
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.one_char | [] | [
99,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_nonempty | [] | [
1633,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1632,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_smul | [] | [
2175,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2173,
1
] |
Mathlib/Data/PNat/Basic.lean | Nat.succPNat_inj | [] | [
104,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/Separation.lean | continuousOn_update_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\ninst✝² : T1Space α\ninst✝¹ : DecidableEq α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nx : α\ny : β\n⊢ (∀ (b : α), b ≠ x → b ∈ s → ContinuousWithinAt (update f x y) s b) ∧ (x ∈ s → ContinuousWithinAt (update f x y) s x) ↔\n Continu... | [
586,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.AwayMap.lift_comp | [] | [
1282,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.multiplicative_factorization' | [
{
"state_after": "case hp\nβ : Type u_1\ninst✝ : CommMonoid β\nf : ℕ → β\nh_mult : ∀ (x y : ℕ), coprime x y → f (x * y) = f x * f y\nhf0 : f 0 = 1\nhf1 : f 1 = 1\n⊢ ∀ (p n : ℕ), Prime p → 0 < n → f (p ^ n) = Finsupp.prod (factorization (p ^ n)) fun p k => f (p ^ k)\n\ncase h0\nβ : Type u_1\ninst✝ : CommMonoid β... | [
906,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.comp_monotoneOn | [] | [
658,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_neg_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.134622\nE : Type ?u.134625\nF : Type u_3\nG : Type ?u.134631\nE' : Type u_2\nF' : Type ?u.134637\nG' : Type ?u.134640\nE'' : Type ?u.134643\nF'' : Type ?u.134646\nG'' : Type ?u.134649\nR : Type ?u.134652\nR' : Type ?u.134655\n𝕜 : Type ?u.134658\n𝕜' : Type ?u.134661\... | [
903,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSet_empty_right | [
{
"state_after": "Ω : Type u_1\nι : Type ?u.648825\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasure μ\ns : Set Ω\n⊢ Indep (generateFrom {s}) ⊥",
"state_before": "Ω : Type u_1\nι : Type ?u.648825\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasur... | [
175,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_idem | [] | [
1187,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.dist_comm_aux | [
{
"state_after": "case intro\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : Reachable G u v\np : Walk G v u\nhp : Walk.length p = dist G v u\n⊢ dist G u v ≤ dist G v u",
"state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\nh : Reachable G u v\n⊢ dist G u v ≤ dist G v u",
"tactic": "obtain ⟨p, hp⟩ ... | [
119,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
9
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_sup_right | [] | [
412,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Order/Atoms.lean | isSimpleOrder_iff_isAtom_top | [] | [
668,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_orbit_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\ng : α\na : β\n⊢ a ∈ orbit α (g • a)",
"tactic": "simp only [orbit_smul, mem_orbit_self]"
}
] | [
260,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/List/Rotate.lean | List.cyclicPermutations_cons | [] | [
581,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bit1_val | [] | [
129,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.det_to_matrix_orthonormalBasis_real | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.1554527\n𝕜 : Type ?u.1554530\ninst✝¹⁰ : IsROrC 𝕜\nE : Type ?u.1554536\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.1554556\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup ... | [
730,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Data/List/Chain.lean | List.chain'_split | [] | [
218,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.coprime_mul_left_right | [] | [
313,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
312,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.add_apply | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | nndist_div_left | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝³ : Group G\ninst✝² : PseudoMetricSpace G\ninst✝¹ : IsometricSMul G G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b c : G\n⊢ nndist (a / b) (a / c) = nndist b c",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
422,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderCobaseChange.unop | [] | [
282,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ ↑sign f⁻¹ = ↑sign f",
"tactic": "rw [MonoidHom.map_inv sign f, Int.units_inv_eq_self]"
}
] | [
570,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.map_modByMonic | [] | [
384,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.map_volume_mul_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2209033\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\n⊢ Measure.map (fun x => x * a) volume = ofReal (abs a⁻¹) • volume",
"tactic": "simpa only [mul_comm] using Real.map_volume_mul_left h"
}
] | [
334,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.ext_iff | [] | [
798,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X_pow_eq_C_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\nn k : ℕ\n⊢ (↑derivative^[k]) (X ^ n) = ↑C ↑(Nat.descFactorial n k) * X ^ (n - k)",
"tactic": "rw [iterate_derivative_X_pow_eq_nat_cast_mul n k, C_eq_nat_cast... | [
514,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.one_lt_card_support_of_ne_one | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : f ≠ 1\n⊢ ∃ a b, ¬(↑f a = a ∨ ↑f b = b ∨ a = b)",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : f ≠ 1\n⊢ 1 < card (support f)",
"tactic": "simp_rw [one_lt_card_... | [
589,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_apply | [] | [
811,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.id_apply | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_inf | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.31660\nP : Type ?u.31663\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv : α → M\nxs : Fin l → M\n⊢ (Realize φ v xs... | [
287,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_sub | [] | [
391,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
11
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_join | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nS : WSeq (WSeq α)\n⊢ Computation.IsBisimulation fun c1 c2 =>\n c1 = c2 ∨ ∃ S, c1 = destruct (join S) ∧ c2 = Computation.bind (destruct S) destruct_join.aux",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nS : WSeq (WSeq α)\n⊢ destruct (join S) =... | [
1557,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_smul_measure | [
{
"state_after": "case hz\nα : Type u_1\nE : Type ?u.1990359\nF : Type u_2\nG : Type ?u.1990365\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\nhp : 0 ≤ p\nf : α → F\nc : ℝ≥0∞\n⊢ 0 ≤ 1 / p",
"sta... | [
606,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | isUnit_map_iff | [] | [
223,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.tail_map | [
{
"state_after": "case intro.intro\nn : ℕ\nα : Type u_2\nβ : Type u_1\nv : Vector α (n + 1)\nf : α → β\na : α\nv' : Vector α n\nh : v = a ::ᵥ v'\n⊢ tail (map f v) = map f (tail v)",
"state_before": "n : ℕ\nα : Type u_2\nβ : Type u_1\nv : Vector α (n + 1)\nf : α → β\n⊢ tail (map f v) = map f (tail v)",
"... | [
114,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
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