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/PNat/Factors.lean | PrimeMultiset.coe_coeNatMonoidHom | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.add | [] | [
665,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | derivWithin_sum | [] | [
188,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.le_sqrt_iff | [] | [
72,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/UniformSpace/CompareReals.lean | CompareReals.compare_uc | [] | [
121,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integrableOn_iUnion_of_summable_integral_norm | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nE : Type u_2\nF : Type ?u.299502\ninst✝² : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : Countable β\nf : α → E\ns : β → Set α\nhs : ∀ (b : β), MeasurableSet (s b)\nhi : ∀ (b : β), IntegrableOn f (s b)\nh : Summable fun b => ∫ (a : α) in s... | [
800,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.nth_of_bisim | [
{
"state_after": "F : PFunctor\nX : Type ?u.60946\nf : X → Obj F X\nR : M F → M F → Prop\ninst✝ : Inhabited (M F)\nbisim : IsBisimulation R\ns₁ s₂ : M F\nps : Path F\nh₀ : R s₁ s₂\nhh : IsPath ps s₁ ∨ IsPath ps s₂\n⊢ iselect ps s₁ = iselect ps s₂ ∧\n ∃ a f f',\n isubtree ps s₁ = M.mk { fst := a, snd := ... | [
694,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.zero_bind | [] | [
245,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_re_zero_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1554514\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ ↑re (inner x 0) = 0",
"tactic"... | [
574,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_add | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : CommRing K\np q : FractionRing K[X]\n⊢ { toFractionRing := p + q } = { toFractionRing := p } + { toFractionRing := q }",
"tactic": "simp only [HAdd.hAdd, Add.add, RatFunc.add]"
}
] | [
329,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.infinite_mul | [] | [
137,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | UniformCauchySeqOn.mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\nι : Type u_3\nl : Filter ι\nl' : Filter β\nf f' : ι → β → α\ng g' : β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nhf' : UniformCauchySeqOn f' l s\nu : Set (α × α)\n... | [
526,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/List/Perm.lean | List.mem_permutations_of_perm_lemma | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ is l : List α\nH : l ~ [] ++ is → (∃ ts' x, l = ts' ++ is) ∨ l ∈ permutationsAux is []\n⊢ l ~ is → l ∈ permutations is",
"tactic": "simpa [permutations, perm_nil] using H"
}
] | [
1240,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.toMulHom_eq_coe | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
src/lean/Init/Core.lean | Function.comp_apply | [] | [
33,
98
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
33,
9
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | Ideal.isOpen_of_open_subideal | [] | [
391,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/RingTheory/Fintype.lean | card_units_lt | [] | [
22,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
20,
1
] |
Mathlib/Topology/GDelta.lean | IsOpen.isGδ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.165\nγ : Type ?u.168\nι : Type ?u.171\ninst✝ : TopologicalSpace α\ns : Set α\nh : IsOpen s\n⊢ ∀ (t : Set α), t ∈ {s} → IsOpen t",
"tactic": "simp [h]"
}
] | [
58,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.coe_nnabs | [] | [
1062,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_mul_monomial' | [
{
"state_after": "case inl\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m✝ : σ\ns✝ : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q : MvPolynomial σ R\nm s : σ →₀ ℕ\np : MvPolynomial σ R\n⊢ coeff m (p * ↑(monomial s) 0) = if s ≤ m then coeff (m - s) ... | [
783,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.mem_normalizer_fintype | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.42200\ninst✝¹ : AddGroup A\nS : Set G\ninst✝ : Finite ↑S\nx : G\nh : ∀ (n : G), n ∈ S → x * n * x⁻¹ ∈ S\nthis : (a : Prop) → Decidable a\n⊢ x ∈ setNormalizer S",
"state_before": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.42200\ninst✝¹ : AddGrou... | [
262,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | nnnorm_surjective | [] | [
366,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_eq_zero_iff | [
{
"state_after": "case empty\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : Nontrivial α\n⊢ lcm 0 = 0 ↔ 0 ∈ 0\n\ncase cons\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : Nontrivial α\na : α\ns : Multiset α\nihs : lcm s = 0... | [
92,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
8
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.IsHomogeneous.coeff_eq_zero | [
{
"state_after": "σ : Type u_1\nτ : Type ?u.155224\nR : Type u_2\nS : Type ?u.155230\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\nm n : ℕ\nhφ : IsHomogeneous φ n\nd : σ →₀ ℕ\nhd : ∑ i in d.support, ↑d i ≠ n\naux : ¬coeff d φ ≠ 0\n⊢ coeff d φ = 0",
"state_before": "σ : Type u_1\nτ : Type ?u.155224\nR : T... | [
173,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | gold_ne_zero | [] | [
114,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₂Γ₂_compatible_with_N₁Γ₀ | [] | [
182,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.IsBounded.fst_of_prod | [] | [
70,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Covering/DensityTheorem.lean | IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\ninst✝⁶ : MetricSpace α\ninst✝⁵ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝⁴ : IsUnifLocDoublingMeasure μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nE : Type u_1\ninst✝ : NormedAddCommG... | [
164,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Matrix/Basic.lean | RingHom.map_matrix_mul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1247421\nm : Type u_1\nn : Type u_2\no : Type u_3\nm' : o → Type ?u.1247435\nn' : o → Type ?u.1247440\nR : Type ?u.1247443\nS : Type ?u.1247446\nα : Type v\nβ : Type w\nγ : Type ?u.1247453\ninst✝² : Fintype n\ninst✝¹ : NonAssocSemiring α\ninst✝ : Non... | [
2937,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2935,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.intermediateFieldMap_symm_apply_coe | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_closure_of_bounded | [] | [
2358,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2355,
1
] |
Mathlib/Data/List/Basic.lean | List.concat_nil | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.map_proj | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.of_zpow | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.205527\nα : Type u_1\nβ : Type ?u.205533\nf g : Perm α\np : α → Prop\nx y z : α\nn : ℤ\nx✝ : SameCycle (f ^ n) x y\nm : ℤ\nh : ↑((f ^ n) ^ m) x = y\n⊢ ↑(f ^ (n * m)) x = y",
"tactic": "simp [zpow_mul, h]"
}
] | [
220,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Topology/SubsetProperties.lean | Set.Finite.isCompact_biUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type u_1\nπ : ι → Type ?u.31333\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t : Set α\ns : Set ι\nf : ι → Set α\nhs : Set.Finite s\nhf : ∀ (i : ι), i ∈ s → IsCompact (f i)\nl : Ultrafilter α\nhl : ∃ i, i ∈ s ∧ f i ∈ l\n⊢ ∃ a, (a ∈ ⋃ (i : ι) (_ : i ∈... | [
412,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | LinearMap.finrank_range_of_inj | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nf : V →ₗ[K] V₂\nhf : Injective ↑f\n⊢ finrank K { x // x ∈ range f } = finrank K V",
"tactic": "rw [(LinearEqui... | [
248,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.ωUnit_coe | [] | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basisFun_equivFun | [] | [
294,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.derivWithin | [] | [
75,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
11
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.degrees_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommRing R\np✝ q✝ : MvPolynomial σ R\ninst✝ : DecidableEq σ\np q : MvPolynomial σ R\n⊢ degrees (p - q) ≤ degrees p ⊔ degrees q",
"tactic": "simpa only [sub_eq_add_neg]... | [
106,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.dropFun_prod | [
{
"state_after": "case a.h\nn : ℕ\nα α' β β' : TypeVec (n + 1)\nf : α ⟹ β\nf' : α' ⟹ β'\ni : Fin2 n\nx✝ : drop (α ⊗ α') i\n⊢ dropFun (f ⊗' f') i x✝ = (dropFun f ⊗' dropFun f') i x✝",
"state_before": "n : ℕ\nα α' β β' : TypeVec (n + 1)\nf : α ⟹ β\nf' : α' ⟹ β'\n⊢ dropFun (f ⊗' f') = (dropFun f ⊗' dropFun f')... | [
747,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.distribMulActionHom_ext' | [] | [
1681,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
] |
Mathlib/Data/List/AList.lean | AList.keys_singleton | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.coeFn_add | [] | [
426,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_sigma_val | [] | [
369,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.thinkN_mem | [] | [
416,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_add_const_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x + a) '' Iio b = Iio (b + a)",
"tactic": "simp"
}
] | [
283,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.rootSet_X_pow | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝³ : Field R\np q : R[X]\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra R S\nn : ℕ\nhn : n ≠ 0\n⊢ 1 ≠ 0",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝³ : Field R\np q... | [
383,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiableAt_sin | [] | [
61,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.modEq_rfl | [] | [
61,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isPwo_empty | [] | [
453,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
9
] |
Mathlib/Algebra/Group/Opposite.lean | MulOpposite.unop_div | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_ofReal_re | [] | [
689,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | NNReal.summable_geometric | [] | [
270,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ClosedEmbedding.measurableEmbedding | [] | [
1029,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean | Real.lt_tan | [
{
"state_after": "x : ℝ\nh1 : 0 < x\nh2 : x < π / 2\nU : Set ℝ := Ico 0 (π / 2)\n⊢ x < tan x",
"state_before": "x : ℝ\nh1 : 0 < x\nh2 : x < π / 2\n⊢ x < tan x",
"tactic": "let U := Ico 0 (π / 2)"
},
{
"state_after": "x : ℝ\nh1 : 0 < x\nh2 : x < π / 2\nU : Set ℝ := Ico 0 (π / 2)\nintU : interior ... | [
120,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/Cover.lean | Covby.Iio_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.38227\ninst✝ : LinearOrder α\na b c : α\nh : a ⋖ b\n⊢ Iio b = Iic a",
"tactic": "rw [← Iic_union_Ioo_eq_Iio h.lt, h.Ioo_eq, union_empty]"
}
] | [
427,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.nontrivial_iff_ne_bot | [
{
"state_after": "case mp\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN✝ N' : LieSubmodule R L M\nI J : LieIdeal R L\nN : LieSubmodule R L M\n⊢ N = ⊥ → ¬N... | [
552,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_of_liftPropAt | [
{
"state_after": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.50373\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... | [
465,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.lt_iff_exists_rat_btwn | [] | [
614,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.HasBasis.limsSup_eq_iInf_sSup | [] | [
665,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/GroupTheory/CommutingProbability.lean | commProb_pos | [] | [
52,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_map_equiv | [] | [
1568,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsCodetecting.mono | [] | [
216,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | Module.End.intCast_apply | [] | [
1091,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ext | [] | [
145,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.lsum_single | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nK : Type u'\nM✝ : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι✝ : Type x\nι' : Type x'\ninst✝¹¹ : Semiring R✝\ninst✝¹⁰ : AddCommMonoid M₂\ninst✝⁹ : Module R✝ M₂\ninst✝⁸ : AddCommMonoid M₃\ninst✝⁷ : Module... | [
170,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMapₛₗ₂'_toMatrix' | [] | [
247,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.add_eq_two_iff | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ m + n = 2 ↔ m = 0 ∧ n = 2 ∨ m = 1 ∧ n = 1 ∨ m = 2 ∧ n = 0",
"tactic": "cases n <;>\nsimp [(succ_ne_zero 1).symm, (show 2 = Nat.succ 1 from rfl),\n succ_eq_add_one, ← add_assoc, succ_inj', add_eq_one_iff]"
}
] | [
202,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_disjiUnion | [
{
"state_after": "ι : Type u_1\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoid β\ns : Finset ι\nt : ι → Finset α\nh : Set.PairwiseDisjoint (↑s) t\n⊢ ∏ x in disjiUnion s t h, f x =\n fold (fun x x_1 => x * x_1) (fold (fun x x_1 => x * x_1) 1 (fun i => 1) s) (fu... | [
399,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Algebra/Hom/Group.lean | map_mul_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.47943\nβ : Type ?u.47946\nM : Type ?u.47949\nN : Type ?u.47952\nP : Type ?u.47955\nG : Type u_1\nH : Type u_2\nF : Type u_3\ninst✝⁴ : MulOneClass M\ninst✝³ : MulOneClass N\ninst✝² : Group G\ninst✝¹ : DivisionMonoid H\ninst✝ : MonoidHomClass F G H\nf ... | [
436,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext | [] | [
466,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.pentagon_inv_hom_hom_hom_hom | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\nh : c ⟶ d\ni : d ⟶ e\n⊢ (α_ f g h).inv ▷ i ≫ (α_ (f ≫ g) h i).hom ≫ (α_ f g (h ≫ i)).hom = (α_ f (g ≫ h) i).hom ≫ f ◁ (α_ g h i).hom",
"tactic": "simp [← cancel_epi ((α_ f g h).hom ▷ i)]"... | [
311,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Std/Logic.lean | iff_of_true | [] | [
59,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_sum | [] | [
530,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousOn.aestronglyMeasurable_of_isSeparable | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nE : Type ?u.1787521\nF : Type ?u.1787524\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : TopologicalSpace α\ninst✝³ : PseudoMetrizableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PseudoMetrizableSpace β\nf : α →... | [
516,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/Finset/Pairwise.lean | Set.PairwiseDisjoint.biUnion_finset | [
{
"state_after": "α : Type u_3\nι : Type u_2\nι' : Type u_1\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\ns : Set ι'\ng : ι' → Finset ι\nf : ι → α\nhs : PairwiseDisjoint s fun i' => sup (g i') f\nhg : ∀ (i : ι'), i ∈ s → PairwiseDisjoint (↑(g i)) f\na : ι\nha : a ∈ ⋃ (i : ι') (_ : i ∈ s), ↑(g i)\nb : ι\nhb : b ∈ ⋃ (... | [
63,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.apply_symm_apply | [] | [
786,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.wEquiv.abs' | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nx y : MvPFunctor.W (P F) α\n⊢ abs (MvPFunctor.wDest' (P F) x) = abs (MvPFunctor.wDest' (P F) y) → WEquiv x y",
"state_before": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : T... | [
119,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsInt.to_raw_eq | [] | [
84,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.covering_of_eq_top | [] | [
139,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_add | [] | [
126,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.gcd_mul_right_cancel_right | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\nH : coprime k m\n⊢ gcd m (n * k) = gcd m n",
"tactic": "rw [Nat.mul_comm n k, H.gcd_mul_left_cancel_right n]"
}
] | [
271,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
269,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.self_eq_zero | [] | [
961,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumDiffSubset_symm_apply_of_mem | [
{
"state_after": "case a\nα✝ : Sort u\nβ : Sort v\nγ : Sort w\nα : Type u_1\ns t : Set α\nh : s ⊆ t\ninst✝ : DecidablePred fun x => x ∈ s\nx : ↑t\nhx : ↑x ∈ s\n⊢ ↑(Set.sumDiffSubset h) (↑(Set.sumDiffSubset h).symm x) =\n ↑(Set.sumDiffSubset h) (Sum.inl { val := ↑x, property := hx })",
"state_before": "α✝... | [
383,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_le_one_of_lt | [] | [
793,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.aemeasurable | [] | [
1216,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
11
] |
Mathlib/Data/Set/Function.lean | Set.injOn_empty | [] | [
602,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Order/OrderIsoNat.lean | RelEmbedding.acc_iff_no_decreasing_seq | [
{
"state_after": "case mp\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\nx : α\n⊢ Acc r x → IsEmpty { f // x ∈ Set.range ↑f }\n\ncase mpr\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\nx : α\n⊢ IsEmpty { f // x ∈ Set.range ↑f } → Acc r x",
"state_before": "α : Type u_1\nr : α → α →... | [
83,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Vector3.lean | Vector3.append_insert | [
{
"state_after": "case refine'_1\nα : Type u_1\nm n : ℕ\na : α\nt : Vector3 α m\nv : Vector3 α n\ni : Fin2 (succ n)\ne✝ : succ n + m = succ (n + m)\ne : succ n + 0 = succ (n + 0)\n⊢ insert a ([] +-+ v) (Eq.recOn e (add i 0)) = Eq.recOn e ([] +-+ insert a v i)\n\ncase refine'_2\nα : Type u_1\nm n : ℕ\na : α\nt✝ ... | [
216,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.mem_rootSet | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\np✝ q : R[X]\ninst✝⁴ : CommRing T\np : T[X]\nS : Type u_1\ninst✝³ : CommRing S\ninst✝² : IsDomain S\ninst✝¹ : Algebra T S\ninst✝ : NoZeroSMulDivisors T S\na : S\n⊢ a ∈... | [
945,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Algebra/Category/ModuleCat/Colimits.lean | ModuleCat.Colimits.cocone_naturality | [
{
"state_after": "case h\nR : Type u\ninst✝¹ : Ring R\nJ : Type w\ninst✝ : Category J\nF : J ⥤ ModuleCat R\nj j' : J\nf : j ⟶ j'\nx✝ : ↑(F.obj j)\n⊢ ↑(F.map f ≫ coconeMorphism F j') x✝ = ↑(coconeMorphism F j) x✝",
"state_before": "R : Type u\ninst✝¹ : Ring R\nJ : Type w\ninst✝ : Category J\nF : J ⥤ ModuleCa... | [
255,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.blocksFun_pos | [] | [
932,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.isClosed_cl | [
{
"state_after": "X : Compactum\nA : Set X.A\n⊢ ∀ (F : Ultrafilter X.A), Compactum.cl A ∈ F → str X F ∈ Compactum.cl A",
"state_before": "X : Compactum\nA : Set X.A\n⊢ IsClosed (Compactum.cl A)",
"tactic": "rw [isClosed_iff]"
},
{
"state_after": "X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\n... | [
287,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/Antichain.lean | IsWeakAntichain.insert | [] | [
379,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
11
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_mul_inner_self_le | [] | [
712,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.exists_rat_pow_btwn_rat | [
{
"state_after": "no goals",
"state_before": "z x✝ y✝ : ℝ\nn : ℕ\nhn : n ≠ 0\nx y : ℚ\nh : x < y\nhy : 0 < y\n⊢ ∃ q, 0 < q ∧ x < q ^ n ∧ q ^ n < y",
"tactic": "apply_mod_cast exists_rat_pow_btwn_rat_aux hn x y <;> assumption"
}
] | [
689,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.neg_apply | [] | [
246,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_center_iff | [] | [
1377,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonneg_cases | [] | [
668,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.