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/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_div | [] | [
497,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.locallyIntegrableOn_iff_locallyIntegrable_restrict | [
{
"state_after": "X : Type u_1\nY : Type ?u.123754\nE : Type u_2\nR : Type ?u.123760\ninst✝⁵ : MeasurableSpace X\ninst✝⁴ : TopologicalSpace X\ninst✝³ : MeasurableSpace Y\ninst✝² : TopologicalSpace Y\ninst✝¹ : NormedAddCommGroup E\nf : X → E\nμ : Measure X\ns : Set X\ninst✝ : OpensMeasurableSpace X\nhs : IsClose... | [
168,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_insertNth | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.120563\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na✝ a b : α\nas : List α\nx✝ : 0 ≤ length as\n⊢ a ∈ insertNth 0 b as ↔ a = b ∨ a ∈ as",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ... | [
1658,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1652,
1
] |
Mathlib/Data/Dfinsupp/Multiset.lean | Dfinsupp.toMultiset_single | [] | [
42,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.zero_apply | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.exists_mem_and_iff | [
{
"state_after": "case mp\nα : Type u\nf g : Filter α\ns t : Set α\nP Q : Set α → Prop\nhP : Antitone P\nhQ : Antitone Q\n⊢ ((∃ u, u ∈ f ∧ P u) ∧ ∃ u, u ∈ f ∧ Q u) → ∃ u, u ∈ f ∧ P u ∧ Q u\n\ncase mpr\nα : Type u\nf g : Filter α\ns t : Set α\nP Q : Set α → Prop\nhP : Antitone P\nhQ : Antitone Q\n⊢ (∃ u, u ∈ f ∧... | [
226,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Dynamics/Flow.lean | isFwInvariant_iff_isInvariant | [] | [
78,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/List/Count.lean | List.count_append | [] | [
233,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.snd_comp_inl | [] | [
524,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformly_iff_tendsto | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF✝ : ι → α → β\nf✝ : α → β\ns s' : Set α\nx : α\np✝ : Filter ι\np' : Filter α\ng : ι → α\nF : ι → α → β\nf : α → β\np : Filter ι\n⊢ TendstoUniformly F f p ↔ Tendsto (fun q => (f q.snd, F q.f... | [
164,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBoundedUnder_le_abs | [] | [
310,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_iUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.8981\ns✝ : Set α\ninst✝¹ : Bornology α\ninst✝ : Finite ι\ns : ι → Set α\n⊢ IsBounded (⋃ (i : ι), s i) ↔ ∀ (i : ι), IsBounded (s i)",
"tactic": "rw [← sUnion_range, isBounded_sUnion (finite_range s), forall_range_iff]"
... | [
300,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_vsub_right | [] | [
1125,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.characteristic_iff_comap_le | [] | [
2009,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2006,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.degree_derivative_le | [
{
"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✝ : Semiring R\np : R[X]\nH : p = 0\n⊢ degree (↑derivative p) = degree p",
"tactic": "rw [H, derivative_zero]"
}
] | [
212,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.covby_add_one | [] | [
89,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.sup_disjoint | [
{
"state_after": "no goals",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nK₁ K₂ : Compacts G\nh : Disjoint ↑K₁ ↑K₂\n⊢ (fun s => ↑(toFun μ s)) (K₁ ⊔ K₂) = (fun s => ↑(toFun μ s)) K₁ + (fun s => ↑(toFun μ s)) K₂",
"tactic": "simp [apply_eq_coe_toFun, μ.sup_disjoint' _ _ h]"
}
... | [
104,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ y ⧏ -x ↔ x ⧏ -y",
"tactic": "rw [← neg_neg x, neg_lf_neg_iff, neg_neg]"
}
] | [
1365,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1365,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.mk_eq_mk | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.postcomp_uniformContinuous | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Type ?u.77663\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝¹ : UniformSpace β\n𝔖 : Set (Set α)\ninst✝ : UniformSpace γ\nf : γ → β\nhf : UniformContinuous f\n⊢ uniformSpace α γ 𝔖 ≤ UniformSpace.comap (↑(ofFun 𝔖) ∘ (fun x x_1 => x ∘ x_1) f ... | [
766,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
11
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.symm_self_conj | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nα : X ≅ Y\nf : End X\n⊢ ↑(conj α.symm) (↑(conj α) f) = f",
"tactic": "rw [← trans_conj, α.self_symm_id, refl_conj]"
}
] | [
111,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.LiftRel.refl | [] | [
47,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.bound_of_antilipschitz | [] | [
145,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderCobaseChange.inl | [] | [
268,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_union | [] | [
358,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Order/Antichain.lean | IsStrongAntichain.preimage | [] | [
325,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.quot_map_mk | [] | [
519,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.cos_eq_iff_quadratic | [
{
"state_after": "z w : ℂ\n⊢ cos z - w = 0 ↔ exp (z * I) ^ 2 - 2 * w * exp (z * I) + 1 = 0",
"state_before": "z w : ℂ\n⊢ cos z = w ↔ exp (z * I) ^ 2 - 2 * w * exp (z * I) + 1 = 0",
"tactic": "rw [← sub_eq_zero]"
},
{
"state_after": "z w : ℂ\n⊢ exp (z * I) * exp (z * I) + 1 - exp (z * I) * 2 * w ... | [
172,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_sInf_dom | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.145087\nf : α → β\nu₁ : Set (UniformSpace α)\nu₂ : UniformSpace β\nu : UniformSpace α\nh₁ : u ∈ u₁\nhf : UniformContinuous f\n⊢ Tendsto (fun x => (f x.fst, f x.snd)) (𝓤 α) (𝓤 β)",
"state_before": "α : Type ua\nβ : Type ub\nγ... | [
1400,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_sup | [
{
"state_after": "x y : ℝ\na b : CauSeq ℚ abs\n⊢ { cauchy := Quotient.mk equiv (a ⊔ b) } =\n match { cauchy := Quotient.mk equiv a }, { cauchy := Quotient.mk equiv b } with\n | { cauchy := x }, { cauchy := y } =>\n { cauchy := Quotient.map₂ (fun x x_1 => x ⊔ x_1) Real.definition.proof_2✝ x y }",
... | [
466,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.add | [
{
"state_after": "R : Type u_1\ninst✝⁴ : Ring R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nU U₁ U₂ : Submodule R M\nx x₁ x₂ y y₁ y₂ z z₁ z₂ : M\nN : Type ?u.55774\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nV V₁ V₂ : Submodule R N\nhxy₁ : Submodule.Quotient.mk x₁ = Submodule.Quotient.mk y₁\n... | [
90,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.strictMono_rpow_of_pos | [
{
"state_after": "z : ℝ\nh : 0 < z\nx y : ℝ≥0∞\nhxy : x < y\n⊢ (fun x => x ^ z) x < (fun x => x ^ z) y",
"state_before": "z : ℝ\nh : 0 < z\n⊢ StrictMono fun x => x ^ z",
"tactic": "intro x y hxy"
},
{
"state_after": "case intro\nz : ℝ\nh : 0 < z\ny : ℝ≥0∞\nx : ℝ≥0\nhxy : ↑x < y\n⊢ (fun x => x ^ ... | [
541,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Fin/SuccPred.lean | Fin.succ_apply | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_mul_snorm_of_ae_le_mul | [] | [
1313,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Order/Hom/Order.lean | OrderHom.sInf_apply | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.map_add_right_Ioc | [
{
"state_after": "α : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ map (fun x => c + x) (Ioc a b) = Ioc (c + a) (c + b)",
"state_before": "α : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFi... | [
321,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_eq_ofFunction | [
{
"state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\nthis : (fun s => ⨆ (_ : Set.Nonempty s), m s) = m\n⊢ ↑(boundedBy m) s = ↑(OuterMeasure.ofFunction m m_empty) s",
"state_before": "α : Type u_1\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\n⊢ ↑(boundedBy m) s = ↑(OuterMeasure.... | [
854,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_sub_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nx : R\n⊢ Separable (X - ↑C x)",
"tactic": "simpa only [sub_eq_add_neg, C_neg] using separable_X_add_C (-x)"
}
] | [
175,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_add_one_pos | [] | [
109,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_nonpos | [] | [
111,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
110,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.factors_left_of_inf_factors | [] | [
410,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lt_aleph0_iff_finite | [
{
"state_after": "no goals",
"state_before": "α✝ β α : Type u\n⊢ (#α) < ℵ₀ ↔ Finite α",
"tactic": "simp only [lt_aleph0, mk_eq_nat_iff, finite_iff_exists_equiv_fin]"
}
] | [
1469,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Split.exact | [
{
"state_after": "case mk.intro.intro.intro.intro.intro.intro\n𝒜 : Type u_1\ninst✝³ : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝² : Preadditive 𝒜\ninst✝¹ : HasKernels 𝒜\ninst✝ : HasImages 𝒜\nφ : B ⟶ A\nχ : C ⟶ B\nh1 : f ≫ g = 0\nh2 : φ ≫ f + g ≫ χ = 𝟙 B\n⊢ Exa... | [
127,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.affine_preimage | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y✝ : E\ns✝ t : Set E\nf : E →ᵃ[𝕜] F\ns : Set F\nhs : StarConvex 𝕜 (↑f x) s\ny : E\nhy : y ∈ ↑f ⁻¹' s\na b : 𝕜\nha : 0 ≤ a\nhb : ... | [
359,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.exists_mem_eq_inf | [] | [
1137,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atTop_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.236788\nι' : Type ?u.236791\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.236800\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\n⊢ Tendsto (fun x => f x * r) l atTop ↔ 0 < r ∧ Tendsto f l atTop ∨ r < 0 ∧ Tendsto f l atBot"... | [
1131,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.iteratedFDeriv_comp_right | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
447,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_div_assoc' | [
{
"state_after": "no goals",
"state_before": "b a c : Int\nh : c ∣ a\n⊢ div (a * b) c = div a c * b",
"tactic": "rw [Int.mul_comm, Int.mul_div_assoc _ h, Int.mul_comm]"
}
] | [
724,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
722,
11
] |
Mathlib/Data/Set/Function.lean | Set.restrict_dite | [] | [
86,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.not_subset_empty | [] | [
464,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Computability/Language.lean | Language.le_add_congr | [] | [
210,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_le_degrees_card | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.350050\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q p : MvPolynomial σ R\n⊢ totalDegree p ≤ ↑Multiset.card (degrees p)",
"tactic": "classical\nrw [totalDegree_eq]\nexact Finset.sup_le fun ... | [
612,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.den_mul | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.ofSet_univ | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.image_coe_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Iio a = Iio ↑a",
"tactic": "rw [← preimage_coe_Iio, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Iio_subset_Iio le_top)]"
}
] | [
100,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.trans | [] | [
100,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.card_sum | [
{
"state_after": "L : Language\nL' : Language\n⊢ ((sum fun i => lift (#Functions L i)) + sum fun i => lift (#Functions L' i)) +\n ((sum fun i => lift (#Relations L i)) + sum fun i => lift (#Relations L' i)) =\n ((sum fun i => lift (#Functions L i)) + sum fun i => lift (#Relations L i)) +\n ((sum fu... | [
271,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.toLp_comp_toContinuousMap | [] | [
1732,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1730,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.symm | [] | [
53,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.id_comp | [] | [
228,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.basisOf_reindex | [
{
"state_after": "case a\nι : Type u_5\nι' : Type u_1\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j✝ : ι\ne : ι ≃ ι'\ni : ι'\nj : { j // j ≠ i }\n⊢ ↑(basisOf (reindex b e) i) j =\n ↑... | [
146,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.zmod_congr_of_sub_mem_span_aux | [
{
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"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nn : ℕ\nx : ℤ_[p]\na b : ℤ\nha : x - ↑a ∈ Ideal.span {↑p ^ n}\nhb : x - ↑b ∈ Ideal.span {↑p ^ n}\n⊢ ↑... | [
152,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.Adj.fst_mem | [] | [
123,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
11
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sum_single | [
{
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2112,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2108,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_floor_of_ne_zero | [] | [
267,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.coeToFun_mul | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Convex.finsum_mem | [
{
"state_after": "R : Type u_3\nE : Type u_2\nF : Type ?u.101329\nι✝ : Type ?u.101332\nι' : Type ?u.101335\nα : Type ?u.101338\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\nin... | [
201,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_some_union_none | [] | [
1203,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_union_filter_neg_eq | [] | [
2961,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2959,
1
] |
Mathlib/Order/Minimal.lean | minimals_idem | [] | [
194,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.tail_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : WSeq α\n⊢ tail (cons a s) = s",
"tactic": "simp [tail]"
}
] | [
710,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_mul_cos_sq | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : (∫ (x : ℝ) in a..b, sin x ^ (2 * 0 + 1) * cos x ^ 2) = ∫ (u : ℝ) in cos b..cos a, u ^ 2 * (1 - u ^ 2) ^ 0\n⊢ (∫ (x : ℝ) in a..b, sin x * cos x ^ 2) = (cos a ^ 3 - cos b ^ 3) / 3",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x * cos x ^ 2) = (cos a ^ 3 ... | [
815,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | cauchySeq_of_le_tendsto_0' | [] | [
1544,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.isUnit_iff | [] | [
234,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_hasStrictFDerivAt_iff | [] | [
326,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_lt_sqrt_iff | [] | [
268,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_one_left' | [] | [
412,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.epi_fst_of_factor_thru_epi_mono_factorization | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : Abelian C\ninst✝² : HasPullbacks C\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ng₁ : Y ⟶ W\ninst✝¹ : Epi g₁\ng₂ : W ⟶ Z\ninst✝ : Mono g₂\nhg : g₁ ≫ g₂ = g\nf' : X ⟶ W\nhf : f' ≫ g₂ = f\nt : PullbackCone f g\nht : IsLimit t\n⊢ Epi... | [
703,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_disjUnion | [] | [
107,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_prod_swap | [
{
"state_after": "α : Type u_1\nα' : Type ?u.2413828\nβ : Type u_2\nβ' : Type ?u.2413834\nγ : Type ?u.2413837\nE : Type u_3\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : MeasurableSpace α'\ninst✝⁷ : MeasurableSpace β\ninst✝⁶ : MeasurableSpace β'\ninst✝⁵ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Measu... | [
348,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/List/Infix.lean | List.inits_reverse | [
{
"state_after": "α : Type u_1\nβ : Type ?u.46786\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ inits (reverse l) = reverse (map reverse (reverse (map reverse (inits (reverse l)))))",
"state_before": "α : Type u_1\nβ : Type ?u.46786\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ inits (reve... | [
407,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.bisim_equiv | [] | [
771,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_neg_eq_neg_num | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.coe_ne_top | [] | [
144,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | ae_lt_of_lt_essInf | [] | [
112,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.union_le_add | [] | [
1843,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1842,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mapsTo_insertNth_face | [
{
"state_after": "ι : Type ?u.314687\nI✝ J : Box ι\nx✝ y✝ : ι → ℝ\nn : ℕ\nI : Box (Fin (n + 1))\ni : Fin (n + 1)\nx : ℝ\nhx : x ∈ Ioc (lower I i) (upper I i)\ny : Fin n → ℝ\nhy : y ∈ ↑(face I i)\n⊢ Fin.insertNth i x y ∈ ↑I",
"state_before": "ι : Type ?u.314687\nI✝ J : Box ι\nx✝ y : ι → ℝ\nn : ℕ\nI : Box (Fi... | [
428,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/SetTheory/Lists.lean | Lists.Equiv.antisymm_iff | [
{
"state_after": "α : Type u_1\nl₁ l₂ : Lists' α true\nh : of' l₁ ~ of' l₂\n⊢ l₁ ⊆ l₂ ∧ l₂ ⊆ l₁",
"state_before": "α : Type u_1\nl₁ l₂ : Lists' α true\n⊢ of' l₁ ~ of' l₂ ↔ l₁ ⊆ l₂ ∧ l₂ ⊆ l₁",
"tactic": "refine' ⟨fun h => _, fun ⟨h₁, h₂⟩ => Equiv.antisymm h₁ h₂⟩"
},
{
"state_after": "case refl\nα... | [
304,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.val_inj | [] | [
163,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_sdiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.306898\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\nh : s₁ ⊆ s₂\n⊢ (∏ x in s₂ \\ s₁, f x) * ∏ x in s₁, f x = ∏ x in s₂, f x",
"tactic": "rw [← prod_union sdiff_disjoint... | [
498,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.toPoly_injective | [] | [
137,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | pow_bit1_pos_iff | [] | [
742,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_p_zpow | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\n⊢ ‖↑p ^ n‖ = ↑p ^ (-n)",
"tactic": "rw [norm_zpow, norm_p, zpow_neg, inv_zpow]"
}
] | [
856,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_singleton | [] | [
2598,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2597,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.snd_map_snd | [
{
"state_after": "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\nM₅ : Type ?u.362883\nM₆ : Type ?u.362886\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np : Sub... | [
673,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_add | [] | [
570,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.Memℒp.snorm_eq_integral_rpow_norm | [
{
"state_after": "α : Type u_2\nE : Type ?u.1137869\nF : Type ?u.1137872\n𝕜 : Type ?u.1137875\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝... | [
1290,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_cond_eq_left | [] | [
836,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_nonneg_of_ae | [
{
"state_after": "α : Type u_1\nE : Type ?u.1063910\nF : Type ?u.1063913\n𝕜 : Type ?u.1063916\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³... | [
1162,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_single_ne_zero | [] | [
362,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
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