name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
Subfield.instIsScalarTowerSubtypeMem | Mathlib.Algebra.Field.Subfield.Basic | ∀ {K : Type u} [inst : DivisionRing K] {X : Type u_1} {Y : Type u_2} [inst_1 : SMul X Y] [inst_2 : SMul K X]
[inst_3 : SMul K Y] [IsScalarTower K X Y] (F : Subfield K), IsScalarTower (↥F) X Y | true |
CategoryTheory.Lax.LaxTrans.isoMk._proof_8 | Mathlib.CategoryTheory.Bicategory.Modification.Lax | ∀ {B : Type u_1} [inst : CategoryTheory.Bicategory B] {C : Type u_5} [inst_1 : CategoryTheory.Bicategory C]
{F G : CategoryTheory.LaxFunctor B C} {η θ : F ⟶ G} (app : (a : B) → η.app a ≅ θ.app a)
(naturality :
∀ {a b : B} (f : a ⟶ b),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRi... | false |
AlgebraicGeometry.Scheme.Hom.mem_smoothLocus | Mathlib.AlgebraicGeometry.Morphisms.Smooth | ∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [inst : AlgebraicGeometry.LocallyOfFinitePresentation f] {x : ↥X},
x ∈ AlgebraicGeometry.Scheme.Hom.smoothLocus f ↔
(CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.stalkMap f x)).FormallySmooth | true |
Complex.arg_exp_mul_I | Mathlib.Analysis.SpecialFunctions.Complex.Arg | ∀ (θ : ℝ), (Complex.exp (↑θ * Complex.I)).arg = toIocMod Real.two_pi_pos (-Real.pi) θ | true |
ContinuousMultilinearMap.smulRight | Mathlib.Topology.Algebra.Module.Multilinear.Basic | {R : Type u} →
{ι : Type v} →
{M₁ : ι → Type w₁} →
{M₂ : Type w₂} →
[inst : CommSemiring R] →
[inst_1 : (i : ι) → AddCommMonoid (M₁ i)] →
[inst_2 : AddCommMonoid M₂] →
[inst_3 : (i : ι) → Module R (M₁ i)] →
[inst_4 : Module R M₂] →
... | true |
AdjoinRoot.liftHom_mk | Mathlib.RingTheory.AdjoinRoot | ∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] (f : Polynomial R) [inst_1 : CommRing S] {a : S}
[inst_2 : Algebra R S] (hfx : (Polynomial.aeval a) f = 0) {g : Polynomial R},
(AdjoinRoot.liftAlgHom f (Algebra.ofId R S) a hfx) ((AdjoinRoot.mk f) g) = (Polynomial.aeval a) g | true |
_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂._simp_1_2 | Mathlib.Data.EReal.Operations | ∀ (x : ℝ), (↑x = ⊤) = False | false |
List.prod_mul_prod_eq_prod_zipWith_mul_prod_drop | Mathlib.Algebra.BigOperators.Group.List.Basic | ∀ {M : Type u_4} [inst : CommMonoid M] (l l' : List M),
l.prod * l'.prod =
(List.zipWith (fun x1 x2 => x1 * x2) l l').prod * (List.drop l'.length l).prod * (List.drop l.length l').prod | true |
Lean.ScopedEnvExtension.State.rec | Lean.ScopedEnvExtension | {σ : Type} →
{motive : Lean.ScopedEnvExtension.State σ → Sort u} →
((state : σ) →
(activeScopes : Lean.NameSet) →
(delimitsLocal : Bool) →
motive { state := state, activeScopes := activeScopes, delimitsLocal := delimitsLocal }) →
(t : Lean.ScopedEnvExtension.State σ) → motive t | false |
Std.LawfulOrderMin.mk | Init.Data.Order.Classes | ∀ {α : Type u} [inst : Min α] [inst_1 : LE α] [toMinEqOr : Std.MinEqOr α] [toLawfulOrderInf : Std.LawfulOrderInf α],
Std.LawfulOrderMin α | true |
Algebra.tensorH1CotangentOfIsLocalization._proof_2 | Mathlib.RingTheory.Etale.Kaehler | ∀ (R : Type u_1) {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
MonoidHomClass ((Algebra.Generators.self R S).toExtension.Ring →+* S) (Algebra.Generators.self R S).toExtension.Ring S | false |
Int.le_floor_add | Mathlib.Algebra.Order.Floor.Ring | ∀ {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] [inst_2 : FloorRing R] [IsStrictOrderedRing R] (a b : R),
⌊a⌋ + ⌊b⌋ ≤ ⌊a + b⌋ | true |
Std.Internal.List.containsKey_maxKey? | Std.Data.Internal.List.Associative | ∀ {α : Type u} {β : α → Type v} [inst : Ord α] [Std.TransOrd α] [inst_2 : BEq α] [Std.LawfulBEqOrd α]
{l : List ((a : α) × β a)},
Std.Internal.List.DistinctKeys l →
∀ {km : α}, Std.Internal.List.maxKey? l = some km → Std.Internal.List.containsKey km l = true | true |
Lean.Language.SnapshotBundle.mk | Lean.Language.Basic | {α : Type} →
Option (Lean.Language.SyntaxGuarded (Lean.Language.SnapshotTask α)) → IO.Promise α → Lean.Language.SnapshotBundle α | true |
Std.IterM.TerminationMeasures.Productive.mk.injEq | Init.Data.Iterators.Basic | ∀ {α : Type w} {m : Type w → Type w'} {β : Type w} [inst : Std.Iterator α m β] (it it_1 : Std.IterM m β),
({ it := it } = { it := it_1 }) = (it = it_1) | true |
CategoryTheory.PreOneHypercover.cylinderX._proof_1 | Mathlib.CategoryTheory.Sites.Hypercover.Homotopy | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {S : C} {E : CategoryTheory.PreOneHypercover S}
{F : CategoryTheory.PreOneHypercover S} (f g : E.Hom F) {i : E.I₀},
CategoryTheory.CategoryStruct.comp (f.h₀ i) (F.f (f.s₀ i)) =
CategoryTheory.CategoryStruct.comp (g.h₀ i) (F.f (g.s₀ i)) | false |
ContinuousMultilinearMap.compContinuousLinearMap._proof_1 | Mathlib.Topology.Algebra.Module.Multilinear.Basic | ∀ {R : Type u_5} {ι : Type u_1} {M₁ : ι → Type u_2} {M₁' : ι → Type u_4} {M₄ : Type u_3} [inst : Semiring R]
[inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : (i : ι) → AddCommMonoid (M₁' i)] [inst_3 : AddCommMonoid M₄]
[inst_4 : (i : ι) → Module R (M₁ i)] [inst_5 : (i : ι) → Module R (M₁' i)] [inst_6 : Module R ... | false |
CategoryTheory.Bicategory.prod._proof_22 | Mathlib.CategoryTheory.Bicategory.Product | ∀ (B : Type u_1) [inst : CategoryTheory.Bicategory B] (C : Type u_2) [inst_1 : CategoryTheory.Bicategory C]
{a b c : B × C} (f : a ⟶ b) (g : b ⟶ c),
CategoryTheory.CategoryStruct.comp
((CategoryTheory.Bicategory.associator f.1 (CategoryTheory.CategoryStruct.id b).1 g.1).prod
(CategoryTheory.Bicatego... | false |
AddCon.list_sum | Mathlib.GroupTheory.Congruence.BigOperators | ∀ {ι : Type u_1} {M : Type u_2} [inst : AddZeroClass M] (c : AddCon M) {l : List ι} {f g : ι → M},
(∀ x ∈ l, c (f x) (g x)) → c (List.map f l).sum (List.map g l).sum | true |
List.nil_eq_flatten_iff | Init.Data.List.Lemmas | ∀ {α : Type u_1} {L : List (List α)}, [] = L.flatten ↔ ∀ l ∈ L, l = [] | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.rec | Lean.Meta.Tactic.Grind.Types | {motive : Lean.Meta.Grind.PendingSolverPropagationsData✝ → Sort u} →
motive Lean.Meta.Grind.PendingSolverPropagationsData.nil✝ →
((solverId : ℕ) →
(lhs rhs : Lean.Expr) →
(rest : Lean.Meta.Grind.PendingSolverPropagationsData✝¹) →
motive rest → motive (Lean.Meta.Grind.PendingSolverPro... | false |
_private.Lean.Meta.DiscrTree.Main.0.Lean.Meta.DiscrTree.reduceUntilBadKey.step._unsafe_rec | Lean.Meta.DiscrTree.Main | Lean.Expr → Lean.MetaM Lean.Expr | false |
Cardinal.mk_set_nat | Mathlib.SetTheory.Cardinal.Continuum | Cardinal.mk (Set ℕ) = Cardinal.continuum | true |
Submodule.comap_equiv_self_of_inj_of_le.match_1 | Mathlib.Algebra.Module.Submodule.Equiv | ∀ {R : Type u_2} {M : Type u_1} {N : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] {f : M →ₗ[R] N} {p : Submodule R N}
(motive : ↥(Submodule.comap f p) → Prop) (x : ↥(Submodule.comap f p)),
(∀ (val : M) (hx : val ∈ Submodule.comap f... | false |
Std.DHashMap.Const.mem_ofList | Std.Data.DHashMap.Lemmas | ∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {β : Type v} [EquivBEq α] [LawfulHashable α] {l : List (α × β)} {k : α},
k ∈ Std.DHashMap.Const.ofList l ↔ (List.map Prod.fst l).contains k = true | true |
CategoryTheory.Localization.Preadditive.add.congr_simp | Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive | ∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Preadditive C]
{L : CategoryTheory.Functor C D} (W W_1 : CategoryTheory.MorphismProperty C) (e_W : W = W_1)
[inst_3 : L.IsLocalization W] [inst_4 : W.HasLeftCalcul... | true |
_private.Mathlib.Order.SupIndep.0.iSupIndep.of_coe_Iic_comp._simp_1_1 | Mathlib.Order.SupIndep | ∀ {ι : Sort u_1} {α : Type u_2} [inst : CompleteLattice α] {a : α} (f : ι → ↑(Set.Iic a)), ⨆ i, ↑(f i) = ↑(⨆ i, f i) | false |
LinearIndepOn.image_of_comp | Mathlib.LinearAlgebra.LinearIndependent.Basic | ∀ {ι : Type u'} {ι' : Type u_1} {R : Type u_2} {s : Set ι} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] (f : ι → ι') (g : ι' → M), LinearIndepOn R (g ∘ f) s → LinearIndepOn R g (f '' s) | true |
CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend | Mathlib.CategoryTheory.Sites.IsSheafFor | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {S : CategoryTheory.Sieve X}
{P : CategoryTheory.Functor Cᵒᵖ (Type v₁)} (h : CategoryTheory.Presieve.IsSheafFor P S.arrows) (f : S.functor ⟶ P),
CategoryTheory.CategoryStruct.comp S.functorInclusion (h.extend f) = f | true |
CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.hasOfPrecompProperty_epimorphisms | Mathlib.CategoryTheory.MorphismProperty.Limits | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C}
[P.IsStableUnderCobaseChange], P.HasOfPrecompProperty (CategoryTheory.MorphismProperty.epimorphisms C) | true |
LeanSearchClient.SearchResult.mk.noConfusion | LeanSearchClient.Syntax | {P : Sort u} →
{name : String} →
{type? docString? doc_url? kind? : Option String} →
{name' : String} →
{type?' docString?' doc_url?' kind?' : Option String} →
{ name := name, type? := type?, docString? := docString?, doc_url? := doc_url?, kind? := kind? } =
{ name := name', ... | false |
Lean.Server.FileWorker.WorkerContext.modifyGetPartialHandler | Lean.Server.FileWorker | {α : Type} →
Lean.Server.FileWorker.WorkerContext →
String → (Lean.Server.FileWorker.PartialHandlerInfo → α × Lean.Server.FileWorker.PartialHandlerInfo) → BaseIO α | true |
GaloisCoinsertion.monotoneIntro._proof_1 | Mathlib.Order.GaloisConnection.Defs | ∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {u : α → β} {l : β → α},
Monotone l → Monotone u → (∀ (a : α), l (u a) ≤ a) → (∀ (b : β), u (l b) = b) → GaloisConnection l u | false |
ContinuousMap.HomotopyRel.symm_bijective | Mathlib.Topology.Homotopy.Basic | ∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f₀ f₁ : C(X, Y)} {S : Set X},
Function.Bijective ContinuousMap.HomotopyRel.symm | true |
isDedekindRing_iff | Mathlib.RingTheory.DedekindDomain.Basic | ∀ (A : Type u_2) [inst : CommRing A] (K : Type u_4) [inst_1 : CommRing K] [inst_2 : Algebra A K] [IsFractionRing A K],
IsDedekindRing A ↔
IsNoetherianRing A ∧ Ring.DimensionLEOne A ∧ ∀ {x : K}, IsIntegral A x → ∃ y, (algebraMap A K) y = x | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.some_getEntryLE_eq_getEntryLE?._simp_1_9 | Std.Data.DTreeMap.Internal.Model | ∀ {α : Type u_1} {a : α} {o : Option α}, some (o.getD a) = o.or (some a) | false |
Complex.equivRealProd | Mathlib.Data.Complex.Basic | ℂ ≃ ℝ × ℝ | true |
IsLocalization.AtPrime.mk'_mem_maximal_iff | Mathlib.RingTheory.Localization.AtPrime.Basic | ∀ {R : Type u_1} [inst : CommSemiring R] (S : Type u_2) [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (I : Ideal R)
[hI : I.IsPrime] [inst_3 : IsLocalization.AtPrime S I] (x : R) (y : ↥I.primeCompl) (h : optParam (IsLocalRing S) ⋯),
IsLocalization.mk' S x y ∈ IsLocalRing.maximalIdeal S ↔ x ∈ I | true |
CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.recOn | Mathlib.CategoryTheory.Monoidal.DayConvolution | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{V : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} V] →
[inst_2 : CategoryTheory.MonoidalCategory C] →
[inst_3 : CategoryTheory.MonoidalCategory V] →
{D : Type u₃} →
[inst_4 : CategoryTheory.Cat... | false |
_private.Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone.0.CochainComplex.mappingCocone.δ_descCochain._proof_1_6 | Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone | ∀ (p : ℤ), p + -1 + 0 = p + -1 | false |
Lean.PrettyPrinter.parenthesizeTerm | Lean.PrettyPrinter.Parenthesizer | Lean.Syntax → Lean.CoreM Lean.Syntax | true |
ENNReal.ofReal_rpow_of_pos | Mathlib.Analysis.SpecialFunctions.Pow.NNReal | ∀ {x p : ℝ}, 0 < x → ENNReal.ofReal x ^ p = ENNReal.ofReal (x ^ p) | true |
Lean.Parser.suppressInsideQuot | Lean.Parser.Basic | Lean.Parser.Parser → Lean.Parser.Parser | true |
Path.Homotopic.equivalence | Mathlib.Topology.Homotopy.Path | ∀ {X : Type u} [inst : TopologicalSpace X] {x₀ x₁ : X}, Equivalence Path.Homotopic | true |
Lean.Elab.Term.LetIdDeclView.recOn | Lean.Elab.Binders | {motive : Lean.Elab.Term.LetIdDeclView → Sort u} →
(t : Lean.Elab.Term.LetIdDeclView) →
((id : Lean.Syntax) →
(binders : Array Lean.Syntax) →
(type value : Lean.Syntax) → motive { id := id, binders := binders, type := type, value := value }) →
motive t | false |
CategoryTheory.Bicategory.postcomposing₂_obj_app_toFunctor_obj | Mathlib.CategoryTheory.Bicategory.Yoneda | ∀ {B : Type u} [inst : CategoryTheory.Bicategory B] (a b : B) (f : a ⟶ b) (x : Bᵒᵖ) (x_1 : Opposite.unop x ⟶ a),
(((CategoryTheory.Bicategory.postcomposing₂ a b).obj f).app x).toFunctor.obj x_1 =
CategoryTheory.CategoryStruct.comp x_1 f | true |
ContFract.instCoeGenContFract | Mathlib.Algebra.ContinuedFractions.Basic | {α : Type u_1} → [inst : One α] → [inst_1 : Zero α] → [inst_2 : LT α] → Coe (ContFract α) (GenContFract α) | true |
CategoryTheory.MonoidalCategory.DayConvolutionUnit.noConfusion | Mathlib.CategoryTheory.Monoidal.DayConvolution | {P : Sort u} →
{C : Type u₁} →
{inst : CategoryTheory.Category.{v₁, u₁} C} →
{V : Type u₂} →
{inst_1 : CategoryTheory.Category.{v₂, u₂} V} →
{inst_2 : CategoryTheory.MonoidalCategory C} →
{inst_3 : CategoryTheory.MonoidalCategory V} →
{F : CategoryTheory.Functor C... | false |
Nat.range_nth_of_infinite | Mathlib.Data.Nat.Nth | ∀ {p : ℕ → Prop}, (setOf p).Infinite → Set.range (Nat.nth p) = setOf p | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.containsKey_filter_iff._simp_1_1 | Std.Data.Internal.List.Associative | ∀ {α : Type u_1} (p : α → Bool) (x : Option α), (Option.any p x = true) = ∃ y, x = some y ∧ p y = true | false |
LinearMap.toMatrix._proof_1 | Mathlib.LinearAlgebra.Matrix.ToLin | ∀ {R : Type u_1} [inst : CommSemiring R] {M₂ : Type u_2} [inst_1 : AddCommMonoid M₂] [inst_2 : Module R M₂],
SMulCommClass R R M₂ | false |
continuous_iff_ultrafilter | Mathlib.Topology.Ultrafilter | ∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Continuous f ↔ ∀ (x : X) (g : Ultrafilter X), ↑g ≤ nhds x → Filter.Tendsto f (↑g) (nhds (f x)) | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.Attr.0.Lean.Elab.Tactic.BVDecide.Frontend.elabBVDecideConfig.match_1 | Lean.Elab.Tactic.BVDecide.Frontend.Attr | (motive :
DoResultPR Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig
PUnit.{1} →
Sort u_1) →
(r :
DoResultPR Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig
PUnit.{1}) →
((a : Le... | false |
NumberField.Units.regOfFamily_div_regulator | Mathlib.NumberTheory.NumberField.Units.Regulator | ∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
(u : Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ),
NumberField.Units.regOfFamily u / NumberField.Units.regulator K =
↑(Subgroup.closure (Set.range u) ⊔ NumberField.Units.torsion K).index | true |
_private.Mathlib.CategoryTheory.WithTerminal.Basic.0.CategoryTheory.WithTerminal.comp.match_1.eq_4 | Mathlib.CategoryTheory.WithTerminal.Basic | ∀ {C : Type u_1}
(motive : CategoryTheory.WithTerminal C → CategoryTheory.WithTerminal C → CategoryTheory.WithTerminal C → Sort u_2)
(x : CategoryTheory.WithTerminal C) (_Y : C)
(h_1 :
(_X _Y _Z : C) →
motive (CategoryTheory.WithTerminal.of _X) (CategoryTheory.WithTerminal.of _Y)
(CategoryTheory... | true |
NNReal.exists_pow_lt_of_lt_one | Mathlib.Data.NNReal.Defs | ∀ {a b : NNReal}, 0 < a → b < 1 → ∃ n, b ^ n < a | true |
IsFractionRing.isAlgebraic_iff | Mathlib.RingTheory.Localization.Integral | ∀ (A : Type u_3) (K : Type u_4) (C : Type u_5) [inst : CommRing A] [IsDomain A] [inst_2 : Field K]
[inst_3 : Algebra A K] [IsFractionRing A K] [inst_5 : CommRing C] [inst_6 : Algebra A C] [inst_7 : Algebra K C]
[IsScalarTower A K C] {x : C}, IsAlgebraic A x ↔ IsAlgebraic K x | true |
Quiver.Path.length_eq_zero_iff._simp_1 | Mathlib.Combinatorics.Quiver.Path.Vertices | ∀ {V : Type u_1} [inst : Quiver V] {a : V} (p : Quiver.Path a a), (p.length = 0) = (p = Quiver.Path.nil) | false |
Sym2.IsDiag._proof_1 | Mathlib.Data.Sym.Sym2 | ∀ {α : Type u_1} (x x_1 : α), (x = x_1) = (x_1 = x) | false |
idRestrGroupoid._proof_3 | Mathlib.Geometry.Manifold.StructureGroupoid | ∀ {H : Type u_1} [inst : TopologicalSpace H],
∃ s, ∃ (h : IsOpen s), OpenPartialHomeomorph.refl H ≈ OpenPartialHomeomorph.ofSet s h | false |
BitVec.ushiftRight_eq_zero | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {x : BitVec w} {n : ℕ}, w ≤ n → x >>> n = 0#w | true |
_private.Mathlib.Tactic.Abel.0.Mathlib.Tactic.Abel.eval._sparseCasesOn_5 | Mathlib.Tactic.Abel | {motive : Lean.Literal → Sort u} →
(t : Lean.Literal) →
((val : ℕ) → motive (Lean.Literal.natVal val)) → (Nat.hasNotBit 1 t.ctorIdx → motive t) → motive t | false |
isSaddlePointOn_value | Mathlib.Order.SaddlePoint | ∀ {E : Type u_1} {F : Type u_2} {β : Type u_3} {X : Set E} {Y : Set F} {f : E → F → β} [inst : CompleteLinearOrder β]
{a : E},
a ∈ X →
∀ {b : F}, b ∈ Y → IsSaddlePointOn X Y f a b → ⨅ x ∈ X, ⨆ y ∈ Y, f x y = f a b ∧ ⨆ y ∈ Y, ⨅ x ∈ X, f x y = f a b | true |
PrimeSpectrum.BasicConstructibleSetData.mk.sizeOf_spec | Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet | ∀ {R : Type u_1} [inst : SizeOf R] (f : R) (n : ℕ) (g : Fin n → R),
sizeOf { f := f, n := n, g := g } = 1 + sizeOf f + sizeOf n | true |
Fin.image_succ_Ioc | Mathlib.Order.Interval.Set.Fin | ∀ {n : ℕ} (i j : Fin n), Fin.succ '' Set.Ioc i j = Set.Ioc i.succ j.succ | true |
_private.Mathlib.NumberTheory.ModularForms.Delta.0.ModularForm.logDeriv_eta_comp_eq_logDeriv_csqrt_eta._proof_1_10 | Mathlib.NumberTheory.ModularForms.Delta | (1 + 1).AtLeastTwo | false |
_private.Init.Data.String.Slice.0.String.Slice.eqIgnoreAsciiCase.go._unary._proof_2 | Init.Data.String.Slice | ∀ (s1 s2 : String.Slice) (s1Curr s2Curr : String.Pos.Raw),
s1Curr < s1.rawEndPos ∧ s2Curr < s2.rawEndPos → s2Curr < s2.rawEndPos | false |
StieltjesFunction.instModuleNNReal._proof_1 | Mathlib.MeasureTheory.Measure.Stieltjes | ∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (c : NNReal) (f : StieltjesFunction R),
Monotone fun x => ↑c * ↑f x | false |
_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone.0.NumberField.mixedEmbedding.fundamentalCone.mem_integerSet._simp_1_2 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | ∀ {α : Type u} (x : α) (a b : Set α), (x ∈ a ∩ b) = (x ∈ a ∧ x ∈ b) | false |
AddValuation.map_lt_sum | Mathlib.RingTheory.Valuation.Basic | ∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedAddCommMonoidWithTop Γ₀] (v : AddValuation R Γ₀)
{ι : Type u_6} {s : Finset ι} {f : ι → R} {g : Γ₀}, g ≠ ⊤ → (∀ i ∈ s, g < v (f i)) → g < v (∑ i ∈ s, f i) | true |
UInt16.toUInt8_ofNatTruncate_of_le | Init.Data.UInt.Lemmas | ∀ {n : ℕ},
UInt16.size ≤ n →
(UInt16.ofNatTruncate n).toUInt8 = UInt8.ofNatLT (UInt8.size - 1) UInt16.toUInt8_ofNatTruncate_of_le._proof_1 | true |
_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Basic | ∀ {α : Type u} {s : Set α} {p : α → Prop} {x : α}, (x ∈ {x | x ∈ s ∧ p x}) = (x ∈ s ∧ p x) | false |
_private.Mathlib.Analysis.InnerProductSpace.Adjoint.0.isStarProjection_iff_eq_starProjection_range._simp_1_2 | Mathlib.Analysis.InnerProductSpace.Adjoint | ∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] {σ₁₂ : R₁ →+* R₂} {M₁ : Type u_4}
[inst_2 : TopologicalSpace M₁] [inst_3 : AddCommMonoid M₁] {M₂ : Type u_6} [inst_4 : TopologicalSpace M₂]
[inst_5 : AddCommMonoid M₂] [inst_6 : Module R₁ M₁] [inst_7 : Module R₂ M₂] {f g : M₁ →SL[σ₁₂] M₂}... | false |
Filter.tendsto_div_const_atBot_iff | Mathlib.Order.Filter.AtTopBot.Field | ∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {l : Filter β}
{f : β → α} {r : α} [l.NeBot],
Filter.Tendsto (fun x => f x / r) l Filter.atBot ↔
0 < r ∧ Filter.Tendsto f l Filter.atBot ∨ r < 0 ∧ Filter.Tendsto f l Filter.atTop | true |
Subgroup.ofUnitsEquivType._proof_3 | Mathlib.Algebra.Group.Submonoid.Units | ∀ {M : Type u_1} [inst : Monoid M] (S : Subgroup Mˣ) (x : ↥S.ofUnits), ↑x ∈ S.ofUnits | false |
Lean.Meta.Grind.SplitStatus.ready | Lean.Meta.Tactic.Grind.Split | ℕ → optParam Bool false → optParam Bool false → Lean.Meta.Grind.SplitStatus | true |
tprod_setProd_singleton_right | Mathlib.Topology.Algebra.InfiniteSum.Constructions | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] (s : Set β) (c : γ)
(f : β × γ → α), ∏' (x : ↑(s ×ˢ {c})), f ↑x = ∏' (b : ↑s), f (↑b, c) | true |
Lean.Export.Entry.ctorIdx | Mathlib.Util.Export | Lean.Export.Entry → ℕ | false |
_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.Data.Atom.mk.injEq | Lean.Elab.DocString.Builtin.Keywords | ∀ (name category name_1 category_1 : Lean.Name),
({ name := name, category := category } = { name := name_1, category := category_1 }) =
(name = name_1 ∧ category = category_1) | true |
LieSubmodule.normalizer._proof_3 | Mathlib.Algebra.Lie.Normalizer | ∀ {R : Type u_2} {L : Type u_3} {M : Type u_1} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [LieModule R L M]
(N : LieSubmodule R L M) (t : R), ∀ m ∈ {m | ∀ (x : L), ⁅x, m⁆ ∈ N}, ∀ (x : L), ⁅x, t • m⁆ ∈ N | false |
Lean.Meta.Grind.TopSort.State._sizeOf_1 | Lean.Meta.Tactic.Grind.EqResolution | Lean.Meta.Grind.TopSort.State → ℕ | false |
Equiv.subtypeProdEquivProd._proof_3 | Mathlib.Logic.Equiv.Prod | ∀ {α : Type u_1} {β : Type u_2} {p : α → Prop} {q : β → Prop} (x : { c // p c.1 ∧ q c.2 }), p (↑x).1 | false |
LinearMap.toContinuousLinearMap.congr_simp | Mathlib.Topology.Algebra.Module.FiniteDimension | ∀ {𝕜 : Type u} [hnorm : NontriviallyNormedField 𝕜] {E : Type v} [inst : AddCommGroup E] [inst_1 : Module 𝕜 E]
[inst_2 : TopologicalSpace E] [inst_3 : IsTopologicalAddGroup E] [inst_4 : ContinuousSMul 𝕜 E] {F' : Type x}
[inst_5 : AddCommGroup F'] [inst_6 : Module 𝕜 F'] [inst_7 : TopologicalSpace F'] [inst_8 : I... | true |
Lean.Compiler.LCNF.NormLevelParam.State.noConfusion | Lean.Compiler.LCNF.Level | {P : Sort u} →
{t t' : Lean.Compiler.LCNF.NormLevelParam.State} →
t = t' → Lean.Compiler.LCNF.NormLevelParam.State.noConfusionType P t t' | false |
List.zipWithLeft'TR.go._unsafe_rec | Batteries.Data.List.Basic | {α : Type u_1} → {β : Type u_2} → {γ : Type u_3} → (α → Option β → γ) → List α → List β → Array γ → List γ × List β | false |
IO.FS.realPath | Init.System.IO | System.FilePath → IO System.FilePath | true |
ShrinkingLemma.PartialRefinement.rec | Mathlib.Topology.ShrinkingLemma | {ι : Type u_1} →
{X : Type u_2} →
[inst : TopologicalSpace X] →
{u : ι → Set X} →
{s : Set X} →
{p : Set X → Prop} →
{motive : ShrinkingLemma.PartialRefinement u s p → Sort u} →
((toFun : ι → Set X) →
(carrier : Set ι) →
(isOp... | false |
SimpleGraph.IsMatchingFree | Mathlib.Combinatorics.SimpleGraph.Matching | {V : Type u_1} → SimpleGraph V → Prop | true |
WeierstrassCurve.Jacobian.negY_eq | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | ∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Jacobian R} (X Y Z : R),
W'.negY ![X, Y, Z] = -Y - W'.a₁ * X * Z - W'.a₃ * Z ^ 3 | true |
invertibleSucc | Mathlib.Algebra.CharP.Invertible | {K : Type u_2} → [inst : DivisionSemiring K] → [CharZero K] → (n : ℕ) → Invertible ↑n.succ | true |
ContinuousMultilinearMap.iteratedFDerivComponent._proof_3 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | ∀ {𝕜 : Type u_5} {ι : Type u_1} {E₁ : ι → Type u_4} {G : Type u_2} [inst : NontriviallyNormedField 𝕜]
[inst_1 : (i : ι) → SeminormedAddCommGroup (E₁ i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E₁ i)]
[inst_3 : SeminormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] [inst_5 : Fintype ι] {α : Type u_3}
[inst_6 : Fintyp... | false |
List.getElem_modifyHead._proof_3 | Init.Data.List.Nat.Modify | ∀ {α : Type u_1} {l : List α} {f : α → α} {i : ℕ}, i < (List.modifyHead f l).length → i < l.length | false |
Lean.Doc.instFromDocArgMessageSeverity | Lean.Elab.DocString | Lean.Doc.FromDocArg Lean.MessageSeverity | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_505 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | Lean.Syntax | false |
List.head_attach | Init.Data.List.Attach | ∀ {α : Type u_1} {xs : List α} (h : xs.attach ≠ []), xs.attach.head h = ⟨xs.head ⋯, ⋯⟩ | true |
_private.Mathlib.NumberTheory.LSeries.AbstractFuncEq.0.WeakFEPair.f_modif_aux2._simp_1_1 | Mathlib.NumberTheory.LSeries.AbstractFuncEq | ∀ {α : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Zero M] [inst_1 : SMulZeroClass R M] (s : Set α) (r : α → R)
(f : α → M), (fun a => r a • s.indicator f a) = s.indicator fun a => r a • f a | false |
_private.Mathlib.Order.KrullDimension.0.Order.exists_series_of_le_height._proof_1_1 | Mathlib.Order.KrullDimension | ∀ {α : Type u_1} [inst : Preorder α] {n : ℕ} (m : ℕ) (p : LTSeries α), p.length = m → n < m → m - n < p.length + 1 | false |
Subalgebra.coe_pi | Mathlib.Algebra.Algebra.Subalgebra.Pi | ∀ {ι : Type u_1} {R : Type u_2} {S : ι → Type u_3} [inst : CommSemiring R] [inst_1 : (i : ι) → Semiring (S i)]
[inst_2 : (i : ι) → Algebra R (S i)] (s : Set ι) (t : (i : ι) → Subalgebra R (S i)),
↑(Subalgebra.pi s t) = (Submodule.pi s fun i => Subalgebra.toSubmodule (t i)).carrier | true |
FinEnum.PSigma.finEnumPropProp._proof_3 | Mathlib.Data.FinEnum | ∀ {α : Prop} {β : α → Prop}, (∃ (a : α), β a) → α | false |
RealRMK.le_rieszMeasure_tsupport_subset | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real | ∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : T2Space X] [inst_2 : MeasurableSpace X] [inst_3 : BorelSpace X]
(Λ : CompactlySupportedContinuousMap X ℝ →ₚ[ℝ] ℝ) [inst_4 : LocallyCompactSpace X]
{f : CompactlySupportedContinuousMap X ℝ},
(∀ (x : X), 0 ≤ f x ∧ f x ≤ 1) → ∀ {V : Set X}, tsupport ⇑f ⊆ V → ENN... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.