name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.RepresentationTheory.Induced.0.Rep.indResHomEquiv._simp_1 | Mathlib.RepresentationTheory.Induced | ∀ {k : Type u_6} {G : Type u_7} {V : Type u_8} {W : Type u_9} [inst : CommRing k] [inst_1 : Group G]
[inst_2 : AddCommGroup V] [inst_3 : Module k V] [inst_4 : AddCommGroup W] [inst_5 : Module k W]
(ρ : Representation k G V) (τ : Representation k G W) (x : V) (y : W) (g : G),
(Representation.Coinvariants.mk (ρ.tpr... | false |
NormalizationMonoid.ofUniqueUnits | Mathlib.Algebra.GCDMonoid.Basic | {α : Type u_1} → [inst : CommMonoidWithZero α] → [Subsingleton αˣ] → NormalizationMonoid α | true |
MonoidHom.toAdditiveRightMulEquiv._proof_1 | Mathlib.Algebra.Group.TypeTags.Hom | ∀ {M : Type u_1} {N : Type u_2} [inst : AddMonoid M] [inst_1 : CommMonoid N] (x x_1 : Multiplicative M →* N),
(MonoidHom.toAdditiveRight.trans Multiplicative.ofAdd).toFun (x * x_1) =
(MonoidHom.toAdditiveRight.trans Multiplicative.ofAdd).toFun (x * x_1) | false |
QuadraticAlgebra.coe_injective | Mathlib.Algebra.QuadraticAlgebra.Defs | ∀ {R : Type u_1} {a b : R} [inst : Zero R], Function.Injective QuadraticAlgebra.C | true |
_private.Batteries.Classes.SatisfiesM.0.SatisfiesM.imp.match_1_1 | Batteries.Classes.SatisfiesM | {α : Type u_1} →
{p : α → Prop} →
(motive : { a // p a } → Sort u_2) → (x : { a // p a }) → ((val : α) → (h : p val) → motive ⟨val, h⟩) → motive x | false |
Matroid.IsStrictMinor.trans | Mathlib.Combinatorics.Matroid.Minor.Order | ∀ {α : Type u_1} {M M' N : Matroid α}, N <m M → M <m M' → N <m M' | true |
Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeff | Mathlib.Algebra.Polynomial.Div | ∀ {R : Type u} [inst : CommRing R] [IsDomain R] {p q : Polynomial R},
p ∣ q → q.natDegree ≤ p.natDegree → q.leadingCoeff ∣ p.leadingCoeff → Associated p q | true |
Lean.Grind.CommRing.Poly | Init.Grind.Ring.CommSolver | Type | true |
TrivSqZeroExt.addMonoid._proof_1 | Mathlib.Algebra.TrivSqZeroExt.Basic | ∀ {R : Type u_1} {M : Type u_2} [inst : AddMonoid R] [inst_1 : AddMonoid M] (a : TrivSqZeroExt R M), 0 + a = a | false |
ContinuousWithinAt.eq_const_of_mem_closure | Mathlib.Topology.Separation.Basic | ∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T1Space Y] {f : X → Y}
{s : Set X} {x : X} {c : Y}, ContinuousWithinAt f s x → x ∈ closure s → (∀ y ∈ s, f y = c) → f x = c | true |
MeasureTheory.OuterMeasure.trim_zero | Mathlib.MeasureTheory.OuterMeasure.Induced | ∀ {α : Type u_1} [inst : MeasurableSpace α], MeasureTheory.OuterMeasure.trim 0 = 0 | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.mk'_obj | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | ∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
(S : CategoryTheory.StrictlyUnitaryLaxFunctorCore B C) (a : B),
(CategoryTheory.StrictlyUnitaryLaxFunctor.mk' S).obj a = S.obj a | true |
_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.simpAppApp?.match_3 | Lean.Compiler.LCNF.Simp.SimpValue | (motive : Option (Lean.Compiler.LCNF.LetDecl Lean.Compiler.LCNF.Purity.pure) → Sort u_1) →
(__x : Option (Lean.Compiler.LCNF.LetDecl Lean.Compiler.LCNF.Purity.pure)) →
((decl : Lean.Compiler.LCNF.LetDecl Lean.Compiler.LCNF.Purity.pure) → motive (some decl)) →
((x : Option (Lean.Compiler.LCNF.LetDecl Lean.Co... | false |
Lean.Parser.Term.doLetRec | Lean.Parser.Do | Lean.Parser.Parser | true |
_private.Lean.Data.RArray.0.Lean.RArray.get_ofFn._proof_1_3 | Lean.Data.RArray | ∀ {n : ℕ} (i : Fin n), ∀ lb ≤ ↑i, ↑i < lb + 1 → ¬lb = ↑i → False | false |
CategoryTheory.SpectralSequence.Hom._sizeOf_1 | Mathlib.Algebra.Homology.SpectralSequence.Basic | {C : Type u_1} →
{inst : CategoryTheory.Category.{u_3, u_1} C} →
{inst_1 : CategoryTheory.Abelian C} →
{κ : Type u_2} →
{c : ℤ → ComplexShape κ} →
{r₀ : ℤ} → {E E' : CategoryTheory.SpectralSequence C c r₀} → [SizeOf C] → [SizeOf κ] → E.Hom E' → ℕ | false |
RingHom.FinitePresentation.of_finiteType | Mathlib.RingTheory.FinitePresentation | ∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [IsNoetherianRing A] {f : A →+* B},
f.FiniteType ↔ f.FinitePresentation | true |
PresentedMonoid.closure_range_of | Mathlib.Algebra.PresentedMonoid.Basic | ∀ {α : Type u_2} (rels : FreeMonoid α → FreeMonoid α → Prop),
Submonoid.closure (Set.range (PresentedMonoid.of rels)) = ⊤ | true |
AddSubgroup.IsSubnormal.below.step | Mathlib.GroupTheory.IsSubnormal | ∀ {G : Type u_2} [inst : AddGroup G] {motive : (a : AddSubgroup G) → a.IsSubnormal → Prop} (H K : AddSubgroup G)
(h_le : H ≤ K) (hSubn : K.IsSubnormal) (hN : (H.addSubgroupOf K).Normal),
AddSubgroup.IsSubnormal.below hSubn → motive K hSubn → AddSubgroup.IsSubnormal.below ⋯ | true |
Setoid.liftEquiv._proof_2 | Mathlib.Data.Setoid.Basic | ∀ {α : Type u_1} {β : Type u_2} (r : Setoid α),
Function.LeftInverse (fun f => ⟨f ∘ Quotient.mk'', ⋯⟩) fun f => Quotient.lift ↑f ⋯ | false |
CategoryTheory.BraidedCategory.curriedBraidingNatIso._proof_2 | Mathlib.CategoryTheory.Monoidal.Braided.Basic | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.BraidedCategory C] (X : C) {X_1 Y : C} (f : X_1 ⟶ Y),
CategoryTheory.CategoryStruct.comp (((CategoryTheory.MonoidalCategory.curriedTensor C).obj X).map f)
((fun Y => β_ X Y) Y).... | false |
Aesop.EqualUpToIds.MVarValue.ctorIdx | Aesop.Util.EqualUpToIds | Aesop.EqualUpToIds.MVarValue → ℕ | false |
MeasureTheory.eLpNorm'_zero' | Mathlib.MeasureTheory.Function.LpSeminorm.Basic | ∀ {α : Type u_1} {m0 : MeasurableSpace α} {q : ℝ} {μ : MeasureTheory.Measure α} {ε : Type u_7}
[inst : TopologicalSpace ε] [inst_1 : ESeminormedAddMonoid ε], q ≠ 0 → μ ≠ 0 → MeasureTheory.eLpNorm' 0 q μ = 0 | true |
Simps.ProjectionRule.add.inj | Mathlib.Tactic.Simps.Basic | ∀ {a : Lean.Name} {a_1 : Lean.Syntax} {a_2 : Lean.Name} {a_3 : Lean.Syntax},
Simps.ProjectionRule.add a a_1 = Simps.ProjectionRule.add a_2 a_3 → a = a_2 ∧ a_1 = a_3 | true |
CategoryTheory.instHasLimitsOfShapeOverOfWithTerminal | Mathlib.CategoryTheory.WithTerminal.Cone | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type w} [inst_1 : CategoryTheory.Category.{w', w} J]
(X : C) [CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.WithTerminal J) C],
CategoryTheory.Limits.HasLimitsOfShape J (CategoryTheory.Over X) | true |
CategoryTheory.AddMonObj.lift_comp_zero_right | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_ | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.AddMonObj B] (f : A ⟶ B)
(g : A ⟶ CategoryTheory.MonoidalCategoryStruct.tensorUnit C),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCat... | true |
CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Page | Lean.Syntax | false |
Matrix.«_aux_Mathlib_LinearAlgebra_Matrix_ConjTranspose___macroRules_Matrix_term_ᴴ_1» | Mathlib.LinearAlgebra.Matrix.ConjTranspose | Lean.Macro | false |
Set.Ioc_disjoint_Ioi | Mathlib.Order.Interval.Set.Disjoint | ∀ {α : Type v} [inst : Preorder α] {a b c : α}, b ≤ c → Disjoint (Set.Ioc a b) (Set.Ioi c) | true |
CategoryTheory.ComposableArrows.homMk₄._proof_3 | Mathlib.CategoryTheory.ComposableArrows.Basic | 2 < 4 + 1 | false |
Lean.Meta.Grind.Goal.hasSameRoot | Lean.Meta.Tactic.Grind.Types | Lean.Meta.Grind.Goal → Lean.Expr → Lean.Expr → Bool | true |
egauge_pi' | Mathlib.Analysis.Convex.EGauge | ∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} [inst : NormedDivisionRing 𝕜] [inst_1 : (i : ι) → AddCommGroup (E i)]
[inst_2 : (i : ι) → Module 𝕜 (E i)] {I : Set ι},
I.Finite →
∀ {U : (i : ι) → Set (E i)},
(∀ i ∈ I, Balanced 𝕜 (U i)) →
∀ (x : (i : ι) → E i),
I = Set.univ ∨ (∃ i ∈... | true |
CyclotomicRing.eq_adjoin_primitive_root | Mathlib.NumberTheory.Cyclotomic.Basic | ∀ (n : ℕ) [NeZero n] (A : Type u) (K : Type w) [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K]
{μ : CyclotomicField n K}, IsPrimitiveRoot μ n → CyclotomicRing n A K = ↥A[μ] | true |
CategoryTheory.yonedaMon._proof_3 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_ | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{M N : CategoryTheory.Mon C} (ψ : M ⟶ N) {M_1 N_1 : Cᵒᵖ} (φ : M_1 ⟶ N_1),
CategoryTheory.CategoryStruct.comp ((CategoryTheory.yonedaMonObj M.X).map φ)
(MonCat.ofHom { toFun := fun x => Category... | false |
Std.ExtDHashMap.filterMap_eq_map | Std.Data.ExtDHashMap.Lemmas | ∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {β : α → Type v} {m : Std.ExtDHashMap α β} {γ : α → Type w}
[inst : EquivBEq α] [inst_1 : LawfulHashable α] {f : (a : α) → β a → γ a},
Std.ExtDHashMap.filterMap (fun k v => some (f k v)) m = Std.ExtDHashMap.map f m | true |
_private.Mathlib.SetTheory.Ordinal.Basic.0.Ordinal.addMonoidWithOne._simp_7 | Mathlib.SetTheory.Ordinal.Basic | ∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (a : α) (b : β),
Sum.Lex r s (Sum.inl a) (Sum.inr b) = True | false |
ISize.ofIntLE_eq_ofIntTruncate | Init.Data.SInt.Lemmas | ∀ {x : ℤ} {h₁ : ISize.minValue.toInt ≤ x} {h₂ : x ≤ ISize.maxValue.toInt}, ISize.ofIntLE x h₁ h₂ = ISize.ofIntTruncate x | true |
CategoryTheory.NatTrans.naturality._autoParam | Mathlib.CategoryTheory.NatTrans | Lean.Syntax | false |
CategoryTheory.Limits.HasWidePushouts | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | (C : Type u) → [CategoryTheory.Category.{v, u} C] → Prop | true |
wbtw_self_iff._simp_1 | Mathlib.Analysis.Convex.Between | ∀ (R : Type u_1) {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] [IsOrderedRing R] {x y : P}, Wbtw R x y x = (y = x) | false |
Lean.Compiler.LCNF.Simp.DiscrM | Lean.Compiler.LCNF.Simp.DiscrM | Type → Type | true |
Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm.casesOn | Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes | {α : ℕ → ℕ → Type} →
{motive : Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm α → Sort u} →
(t : Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm α) →
((getElem : {n m : ℕ} → α n m → ℕ → ℕ → ℚ) →
(setElem : {n m : ℕ} → α n m → ℕ → ℕ → ℚ → α n m) →
(g... | false |
VertexOperator.ncoeff_apply | Mathlib.Algebra.Vertex.VertexOperator | ∀ {R : Type u_1} {V : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup V] [inst_2 : Module R V]
(A : VertexOperator R V) (n : ℤ), VertexOperator.ncoeff A n = HVertexOperator.coeff A (-n - 1) | true |
Lean.TrailingParserDescr | Init.Prelude | Type | true |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss.0.Polynomial.Chebyshev.sumZeroes_T_of_not_dvd._proof_1_9 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss | ∀ {n : ℕ} {k : ℤ},
¬2 * ↑n ∣ k →
n ≠ 0 →
Complex.exp (↑k / ↑n * ↑Real.pi * Complex.I) = Complex.exp (↑k / (2 * ↑n) * ↑Real.pi * Complex.I) ^ 2 →
¬Complex.exp (↑k / (2 * ↑n) * ↑Real.pi * Complex.I) ^ 2 - 1 = 0 ∧
¬1 - Complex.exp (↑k / (2 * ↑n) * ↑Real.pi * Complex.I) ^ 2 = 0 | false |
Asymptotics.instTransForallIsBigOIsTheta | Mathlib.Analysis.Asymptotics.Theta | {α : Type u_1} →
{E : Type u_3} →
{G : Type u_5} →
{F' : Type u_7} →
[inst : Norm E] →
[inst_1 : Norm G] →
[inst_2 : SeminormedAddCommGroup F'] →
{l : Filter α} → Trans (Asymptotics.IsBigO l) (Asymptotics.IsTheta l) (Asymptotics.IsBigO l) | true |
FreeGroup.Red.eq_1 | Mathlib.GroupTheory.FreeGroup.Basic | ∀ {α : Type u}, FreeGroup.Red = Relation.ReflTransGen FreeGroup.Red.Step | true |
String.utf8Len.eq_def | Batteries.Data.String.Lemmas | ∀ (x : List Char),
String.utf8Len x =
match x with
| [] => 0
| c :: cs => String.utf8Len cs + c.utf8Size | true |
_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._proof_2 | Mathlib.Data.EReal.Operations | ∀ (α : Q(Type)) (pα : Q(PartialOrder «$α»)) (__defeqres : PLift («$pα» =Q instPartialOrderEReal)),
«$pα» =Q instPartialOrderEReal | false |
Std.Tactic.BVDecide.BVExpr.WithCache.ctorIdx | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | {α : Type u} → {aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit} → Std.Tactic.BVDecide.BVExpr.WithCache α aig → ℕ | false |
PrincipalSeg.ofElement_toFun | Mathlib.Order.InitialSeg | ∀ {α : Type u_4} (r : α → α → Prop) (a : α) (self : { x // r x a }), (PrincipalSeg.ofElement r a).toFun self = ↑self | true |
Equiv.Perm.Basis.rec | Mathlib.GroupTheory.Perm.Centralizer | {α : Type u_1} →
[inst : DecidableEq α] →
[inst_1 : Fintype α] →
{g : Equiv.Perm α} →
{motive : g.Basis → Sort u} →
((toFun : ↥g.cycleFactorsFinset → α) →
(mem_support_self' : ∀ (c : ↥g.cycleFactorsFinset), toFun c ∈ (↑c).support) →
motive { toFun := toFun, me... | false |
Nat.dfold_add._proof_16 | Init.Data.Nat.Fold | ∀ {n m : ℕ}, ∀ i ≤ n, i ≤ n + m | false |
Lean.Grind.CommRing.Mon.revlexFuel.induct_unfolding | Init.Grind.Ring.CommSolver | ∀ (motive : ℕ → Lean.Grind.CommRing.Mon → Lean.Grind.CommRing.Mon → Ordering → Prop),
(∀ (m₁ m₂ : Lean.Grind.CommRing.Mon), motive 0 m₁ m₂ (m₁.revlexWF m₂)) →
(∀ (fuel : ℕ), motive fuel.succ Lean.Grind.CommRing.Mon.unit Lean.Grind.CommRing.Mon.unit Ordering.eq) →
(∀ (fuel : ℕ) (p : Lean.Grind.CommRing.Power... | true |
_private.Std.Data.Iterators.Lemmas.Producers.Repeat.0.Nat.repeat.match_1.splitter | Std.Data.Iterators.Lemmas.Producers.Repeat | {α : Type u_2} →
(motive : ℕ → α → Sort u_1) →
(x : ℕ) → (x_1 : α) → ((a : α) → motive 0 a) → ((n : ℕ) → (a : α) → motive n.succ a) → motive x x_1 | true |
Ideal.span_range_eq_span_range_support | Mathlib.RingTheory.Ideal.Span | ∀ {α : Type u} [inst : Semiring α] {ι : Type u_1} (x : ι → α),
Ideal.span (Set.range x) = Ideal.span (Set.range fun i => x ↑i) | true |
MulActionHomClass.eq_1 | Mathlib.GroupTheory.GroupAction.Hom | ∀ (F : Type u_8) (M : Type u_9) (X : Type u_10) (Y : Type u_11) [inst : SMul M X] [inst_1 : SMul M Y]
[inst_2 : FunLike F X Y], MulActionHomClass F M X Y = MulActionSemiHomClass F id X Y | true |
Std.DHashMap.Raw.Equiv.constInsertMany_list | Std.Data.DHashMap.RawLemmas | ∀ {α : Type u} [inst : BEq α] [inst_1 : Hashable α] {β : Type v} {m₁ m₂ : Std.DHashMap.Raw α fun x => β} [EquivBEq α]
[LawfulHashable α],
m₁.WF →
m₂.WF →
∀ (l : List (α × β)),
m₁.Equiv m₂ → (Std.DHashMap.Raw.Const.insertMany m₁ l).Equiv (Std.DHashMap.Raw.Const.insertMany m₂ l) | true |
CategoryTheory.Functor.isoWhiskerRight_left_assoc | Mathlib.CategoryTheory.Whiskering | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] {B : Type u₄}
[inst_3 : CategoryTheory.Category.{v₄, u₄} B] (F : CategoryTheory.Functor B C) {G H : CategoryTheory.Functor C D}
(α : G... | true |
HomologicalComplex.homologicalComplexToDGO | Mathlib.Algebra.Homology.DifferentialObject | {β : Type u_1} →
[inst : AddCommGroup β] →
(b : β) →
(V : Type u_2) →
[inst_1 : CategoryTheory.Category.{v_1, u_2} V] →
[inst_2 : CategoryTheory.Limits.HasZeroMorphisms V] →
CategoryTheory.Functor (HomologicalComplex V (ComplexShape.up' b))
(CategoryTheory.Differe... | true |
Lean.Lsp.SymbolInformation.containerName? | Lean.Data.Lsp.LanguageFeatures | Lean.Lsp.SymbolInformation → Option String | true |
Fin.insertNthEquiv_last | Mathlib.Data.Fin.Tuple.Basic | ∀ (n : ℕ) (α : Type u_3), Fin.insertNthEquiv (fun x => α) (Fin.last n) = Fin.snocEquiv fun x => α | true |
Int.inductionOn'_add_one | Mathlib.Data.Int.Basic | ∀ {C : ℤ → Sort u_1} {z b : ℤ} {H0 : C b} {Hs : (k : ℤ) → b ≤ k → C k → C (k + 1)}
{Hp : (k : ℤ) → k ≤ b → C k → C (k - 1)} (hz : b ≤ z),
Int.inductionOn' (z + 1) b H0 Hs Hp = Hs z hz (Int.inductionOn' z b H0 Hs Hp) | true |
ProbabilityTheory.Kernel.integral_deterministic' | Mathlib.Probability.Kernel.Integral | ∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {E : Type u_3}
[inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : β → E} {a : α} [CompleteSpace E] {g : α → β}
(hg : Measurable g),
MeasureTheory.StronglyMeasurable f → ∫ (x : β), f x ∂(ProbabilityTheory.Kernel.determinis... | true |
CategoryTheory.Limits.MonoFactorisation.e | Mathlib.CategoryTheory.Limits.Shapes.Images | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} → {f : X ⟶ Y} → (self : CategoryTheory.Limits.MonoFactorisation f) → X ⟶ self.I | true |
List.min_singleton | Init.Data.List.MinMax | ∀ {α : Type u_1} [inst : Min α] {x : α}, [x].min ⋯ = x | true |
Multiset.zero_product | Mathlib.Data.Multiset.Bind | ∀ {α : Type u_1} {β : Type v} (t : Multiset β), 0 ×ˢ t = 0 | true |
ChevalleyThm.MvPolynomialC.degBound_casesOn_succ._mutual | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | ∀ (k₀ k : ℕ) (D : ℕ → ℕ) (x : ℕ ⊕' ℕ),
PSum.casesOn x
(fun _x =>
ChevalleyThm.MvPolynomialC.degBound k₀ (fun t => Nat.casesOn t k D) (_x + 1) =
(k₀ * k) ^ (k₀ * k) * ChevalleyThm.MvPolynomialC.degBound (k₀ * k) ((k₀ * k) ^ (k₀ * k) • D) _x)
fun _x =>
ChevalleyThm.MvPolynomialC.numBound k₀ (f... | false |
Directed.le_sequence | Mathlib.Logic.Encodable.Basic | ∀ {α : Type u_1} {β : Type u_2} [inst : Encodable α] [inst_1 : Inhabited α] [inst_2 : Preorder β] {f : α → β}
(hf : Directed (fun x1 x2 => x1 ≤ x2) f) (a : α), f a ≤ f (Directed.sequence f hf (Encodable.encode a + 1)) | true |
List.tailsTR.go.eq_def | Batteries.Data.List.Basic | ∀ {α : Type u_1} (l : List α) (acc : Array (List α)),
List.tailsTR.go l acc =
match l with
| [] => acc.toListAppend [[]]
| head :: xs => List.tailsTR.go xs (acc.push l) | true |
_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator._proof_1_2 | Mathlib.Data.Finsupp.Indicator | ∀ {ι : Type u_1} {α : Type u_2} [inst : Zero α] (s : Finset ι) {t : Finset ι} (f : (i : ι) → i ∈ s → α)
[inst_1 : DecidableEq ι],
(Finsupp.indicator t fun i x => (Finsupp.indicator s f) i) = Finsupp.indicator (s ∩ t) fun i hi => f i ⋯ | false |
BialgCat.mk | Mathlib.Algebra.Category.BialgCat.Basic | {R : Type u} →
[inst : CommRing R] →
(carrier : Type v) → [instRing : Ring carrier] → [instBialgebra : Bialgebra R carrier] → BialgCat R | true |
Std.TreeSet.Raw.le_maxD_of_contains | Std.Data.TreeSet.Raw.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet.Raw α cmp} [Std.TransCmp cmp],
t.WF → ∀ {k : α}, t.contains k = true → ∀ {fallback : α}, (cmp k (t.maxD fallback)).isLE = true | true |
AffineSubspace.SOppSide.trans_wSameSide | Mathlib.Analysis.Convex.Side | ∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R]
[inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P]
{s : AffineSubspace R P} {x y z : P}, s.SOppSide x y → s.WSameSide y z → s.WOppSide x z | true |
SupBotHom.dual_comp | Mathlib.Order.Hom.BoundedLattice | ∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : Max α] [inst_1 : Bot α] [inst_2 : Max β] [inst_3 : Bot β]
[inst_4 : Max γ] [inst_5 : Bot γ] (g : SupBotHom β γ) (f : SupBotHom α β),
SupBotHom.dual (g.comp f) = (SupBotHom.dual g).comp (SupBotHom.dual f) | true |
UInt16.le_refl._simp_1 | Init.Data.UInt.Lemmas | ∀ (a : UInt16), (a ≤ a) = True | false |
AlexDisc.recOn | Mathlib.Topology.Order.Category.AlexDisc | {motive : AlexDisc → Sort u} →
(t : AlexDisc) →
((toTopCat : TopCat) →
[is_alexandrovDiscrete : AlexandrovDiscrete ↑toTopCat] →
motive { toTopCat := toTopCat, is_alexandrovDiscrete := is_alexandrovDiscrete }) →
motive t | false |
_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ._simp_1_1 | Mathlib.Data.Fintype.Prod | ∀ {α : Type u_1} [inst : Fintype α] {s : Finset α}, (s = Finset.univ) = ∀ (x : α), x ∈ s | false |
PowerSeries.exp_pow_eq_rescale_exp | Mathlib.RingTheory.PowerSeries.Exp | ∀ {A : Type u_4} [inst : CommRing A] [inst_1 : Algebra ℚ A] (k : ℕ),
PowerSeries.exp A ^ k = (PowerSeries.rescale ↑k) (PowerSeries.exp A) | true |
ContinuousMulEquiv.eq_symm_comp | Mathlib.Topology.Algebra.ContinuousMonoidHom | ∀ {M : Type u_1} {N : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace N] [inst_2 : Mul M]
[inst_3 : Mul N] {α : Type u_3} (e : M ≃ₜ* N) (f : α → M) (g : α → N), f = ⇑e.symm ∘ g ↔ ⇑e ∘ f = g | true |
QuotientGroup.preimage_image_mk | Mathlib.GroupTheory.Coset.Defs | ∀ {α : Type u_1} [inst : Group α] (N : Subgroup α) (s : Set α),
QuotientGroup.mk ⁻¹' (QuotientGroup.mk '' s) = ⋃ x, (fun x_1 => x_1 * ↑x) ⁻¹' s | true |
ZFSet.singleton_inj._simp_1 | Mathlib.SetTheory.ZFC.Basic | ∀ {x y : ZFSet.{u_1}}, ({x} = {y}) = (x = y) | false |
CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | ∀ {J : CategoryTheory.Limits.MultispanShape} (a b : J.L),
Subsingleton (CategoryTheory.Limits.WalkingMultispan.left a ⟶ CategoryTheory.Limits.WalkingMultispan.left b) | true |
ENNReal.isConjExponent_iff_eq_conjExponent | Mathlib.Data.Real.ConjExponents | ∀ {p q : ENNReal}, 1 ≤ p → (p.HolderConjugate q ↔ q = 1 + (p - 1)⁻¹) | true |
_private.Mathlib.Algebra.Category.Ring.Basic.0.CommSemiRingCat.Hom.ext.match_1 | Mathlib.Algebra.Category.Ring.Basic | ∀ {R S : CommSemiRingCat} (motive : R.Hom S → Prop) (h : R.Hom S),
(∀ (hom' : ↑R →+* ↑S), motive { hom' := hom' }) → motive h | false |
CategoryTheory.MorphismProperty.rlp_isStableUnderProductsOfShape | Mathlib.CategoryTheory.MorphismProperty.LiftingProperty | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (T : CategoryTheory.MorphismProperty C) (J : Type u_1),
T.rlp.IsStableUnderProductsOfShape J | true |
Aesop.GoalData.mvars | Aesop.Tree.Data | {Rapp MVarCluster : Type} → Aesop.GoalData Rapp MVarCluster → Aesop.UnorderedArraySet Lean.MVarId | true |
UInt64.toUInt32_toUSize | Init.Data.UInt.Lemmas | ∀ (n : UInt64), n.toUSize.toUInt32 = n.toUInt32 | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.foldl_eq_foldl_toList._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {x : Ord α} {x_1 : BEq α} [Std.LawfulBEqOrd α] {a b : α}, (compare a b = Ordering.eq) = ((a == b) = true) | false |
CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq_id | Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant | ∀ {J : Type u_1} {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} J]
[inst_1 : CategoryTheory.Category.{v_2, u_2} C] {F : CategoryTheory.Functor J C} {i₀ : J}
(h : F.IsEventuallyConstantFrom i₀) [inst_2 : CategoryTheory.IsFiltered J],
h.coconeιApp i₀ = CategoryTheory.CategoryStruct.id (F.obj i₀) | true |
Std.Rcc.Sliceable.recOn | Init.Data.Slice.Notation | {α : Type u} →
{β : Type v} →
{γ : Type w} →
{motive : Std.Rcc.Sliceable α β γ → Sort u_1} →
(t : Std.Rcc.Sliceable α β γ) → ((mkSlice : α → Std.Rcc β → γ) → motive { mkSlice := mkSlice }) → motive t | false |
String.Pos.prev! | Init.Data.String.FindPos | {s : String} → s.Pos → s.Pos | true |
CategoryTheory.Sum.swapCompInl | Mathlib.CategoryTheory.Sums.Basic | (C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(D : Type u₂) →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(CategoryTheory.Sum.inl_ C D).comp (CategoryTheory.Sum.swap C D) ≅ CategoryTheory.Sum.inr_ D C | true |
Cardinal.power_mul | Mathlib.SetTheory.Cardinal.Order | ∀ {a b c : Cardinal.{u_1}}, a ^ (b * c) = (a ^ b) ^ c | true |
Batteries.BinomialHeap.Imp.FindMin.mk | Batteries.Data.BinomialHeap.Basic | {α : Type u_1} →
(Batteries.BinomialHeap.Imp.Heap α → Batteries.BinomialHeap.Imp.Heap α) →
α → Batteries.BinomialHeap.Imp.HeapNode α → Batteries.BinomialHeap.Imp.Heap α → Batteries.BinomialHeap.Imp.FindMin α | true |
Matrix.SpecialLinearGroup.map_intCast_injective | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | ∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] [CharZero R],
Function.Injective ⇑(Matrix.SpecialLinearGroup.map (Int.castRingHom R)) | true |
MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder | Mathlib.RingTheory.MvPowerSeries.Order | ∀ {σ : Type u_1} (w : σ → ℕ) {R : Type u_3} [inst : Ring R] {f g : MvPowerSeries σ R} {d : σ →₀ ℕ},
↑((Finsupp.weight w) d) < MvPowerSeries.weightedOrder w g →
(MvPowerSeries.coeff d) (f * (1 - g)) = (MvPowerSeries.coeff d) f | true |
DirichletCharacter.LSeries_ne_zero_of_one_lt_re | Mathlib.NumberTheory.LSeries.Dirichlet | ∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ}, 1 < s.re → LSeries (fun n => χ ↑n) s ≠ 0 | true |
ContinuousAffineMap.instSub._proof_1 | Mathlib.Topology.Algebra.ContinuousAffineMap | ∀ {R : Type u_4} {V : Type u_3} {W : Type u_2} {P : Type u_1} [inst : Ring R] [inst_1 : AddCommGroup V]
[inst_2 : Module R V] [inst_3 : TopologicalSpace P] [inst_4 : AddTorsor V P] [inst_5 : AddCommGroup W]
[inst_6 : Module R W] [inst_7 : TopologicalSpace W] [IsTopologicalAddGroup W] (f g : P →ᴬ[R] W),
Continuous... | false |
Equiv.apply_swap_eq_self | Mathlib.Logic.Equiv.Basic | ∀ {α : Sort u_1} {β : Sort u_4} [inst : DecidableEq α] {v : α → β} {i j : α},
v i = v j → ∀ (k : α), v ((Equiv.swap i j) k) = v k | true |
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