name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
String.Pos.Raw.instLTCiOfNatInt | Init.Data.String.OrderInstances | Lean.Grind.ToInt.LT String.Pos.Raw (Lean.Grind.IntInterval.ci 0) | true |
Std.DTreeMap.Internal.Impl.Const.get?_congr | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {instOrd : Ord α} {β : Type v} {t : Std.DTreeMap.Internal.Impl α fun x => β} [Std.TransOrd α],
t.WF →
∀ {a b : α},
compare a b = Ordering.eq → Std.DTreeMap.Internal.Impl.Const.get? t a = Std.DTreeMap.Internal.Impl.Const.get? t b | true |
_private.Mathlib.Topology.Baire.LocallyCompactRegular.0.BaireSpace.of_t2Space_locallyCompactSpace._simp_2 | Mathlib.Topology.Baire.LocallyCompactRegular | ∀ {α : Type u} (x : α) (a b : Set α), (x ∈ a ∩ b) = (x ∈ a ∧ x ∈ b) | false |
Matrix.detp_smul_adjp | Mathlib.LinearAlgebra.Matrix.SemiringInverse | ∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
{A B : Matrix n n R},
A * B = 1 →
A + (Matrix.detp 1 A • Matrix.adjp (-1) B + Matrix.detp (-1) A • Matrix.adjp 1 B) =
Matrix.detp 1 A • Matrix.adjp 1 B + Matrix.detp (-1) A • Matrix.adjp (-1) B | true |
Std.DHashMap.Internal.AssocList.foldrM | Std.Data.DHashMap.Internal.AssocList.Basic | {α : Type u} →
{β : α → Type v} →
{δ : Type w} →
{m : Type w → Type w'} → [Monad m] → ((a : α) → β a → δ → m δ) → δ → Std.DHashMap.Internal.AssocList α β → m δ | true |
CategoryTheory.Limits.isCokernelEpiComp._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{X Y : C} {f : X ⟶ Y} {c : CategoryTheory.Limits.CokernelCofork f} {W : C} (g : W ⟶ X) {h : W ⟶ Y},
h = CategoryTheory.CategoryStruct.comp g f →
CategoryTheory.CategoryStruct.comp h (CategoryTheory... | false |
_private.Mathlib.Analysis.CStarAlgebra.Multiplier.0.DoubleCentralizer.instCStarRing._simp_2 | Mathlib.Analysis.CStarAlgebra.Multiplier | ∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : NormedAddCommGroup E]
[inst_1 : SeminormedAddCommGroup F] [inst_2 : DenselyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜₂]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂]
(f ... | false |
CategoryTheory.Limits.isIsoZeroEquiv._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(X Y : C),
CategoryTheory.CategoryStruct.id X = 0 ∧ CategoryTheory.CategoryStruct.id Y = 0 →
CategoryTheory.CategoryStruct.comp 0 0 = CategoryTheory.CategoryStruct.id X ∧
CategoryTheory.Categ... | false |
_private.Std.Time.Format.Basic.0.Std.Time.leftPad | Std.Time.Format.Basic | ℕ → Char → String → String | true |
_private.Mathlib.LinearAlgebra.Matrix.FixedDetMatrices.0.FixedDetMatrices.reduce_mem_reps._simp_1_6 | Mathlib.LinearAlgebra.Matrix.FixedDetMatrices | ∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] [AddRightMono α] {a b : α}, (b ≤ -a) = (a ≤ -b) | false |
_private.Mathlib.Tactic.Linter.Style.0.Mathlib.Linter.Style.longLine.longLineLinter | Mathlib.Tactic.Linter.Style | Lean.Linter | true |
SemimoduleCat.Hom._sizeOf_1 | Mathlib.Algebra.Category.ModuleCat.Semi | {R : Type u} → {inst : Semiring R} → {M N : SemimoduleCat R} → [SizeOf R] → M.Hom N → ℕ | false |
UInt16.fromExpr | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | Lean.Expr → Lean.Meta.SimpM (Option UInt16) | true |
Std.Http.Chunk.ExtensionName.ctorIdx | Std.Internal.Http.Data.Chunk | Std.Http.Chunk.ExtensionName → ℕ | false |
InfHom.id.eq_1 | Mathlib.Order.Hom.Lattice | ∀ (α : Type u_2) [inst : Min α], InfHom.id α = { toFun := id, map_inf' := ⋯ } | true |
Action.instConcreteCategoryHomSubtypeV | Mathlib.CategoryTheory.Action.Basic | (V : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} V] →
(G : Type u_2) →
[inst_1 : Monoid G] →
{FV : V → V → Type u_3} →
{CV : V → Type u_4} →
[inst_2 : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)] →
[inst_3 : CategoryTheory.ConcreteCategory V FV] →
... | true |
SemidirectProduct.inr_splitting | Mathlib.GroupTheory.GroupExtension.Defs | {N : Type u_1} →
{G : Type u_3} →
[inst : Group G] → [inst_1 : Group N] → (φ : G →* MulAut N) → (SemidirectProduct.toGroupExtension φ).Splitting | true |
Equiv.ord_def | Mathlib.Logic.Equiv.Defs | ∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) [inst : Ord β] (a b : α), compare a b = compare (e a) (e b) | true |
TensorAlgebra.GradedAlgebra.ι_apply._proof_1 | Mathlib.LinearAlgebra.TensorAlgebra.Grading | ∀ (R : Type u_1) (M : Type u_2) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (m : M),
(TensorAlgebra.ι R) m ∈ (TensorAlgebra.ι R).range ^ 1 | false |
CategoryTheory.Functor.FullyFaithful.addGrpObj | Mathlib.CategoryTheory.Monoidal.Grp_ | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
{D : Type u₂} →
[inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
[inst_3 : CategoryTheory.CartesianMonoidalCategory D] →
{F : CategoryTheory.Functor C D} →
... | true |
CartanMatrix.E₈ | Mathlib.Data.Matrix.Cartan | Matrix (Fin 8) (Fin 8) ℤ | true |
Mathlib.Tactic.Translate.Config.doc._default | Mathlib.Tactic.Translate.Core | Option String | false |
_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.infs_aux | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | ∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : DecidableEq α] {s t : Finset α} {a : α},
a ∈ lowerClosure ↑(s ⊼ t) ↔ a ∈ lowerClosure ↑s ∧ a ∈ lowerClosure ↑t | true |
NonAssocRing.toAddCommGroupWithOne | Mathlib.Algebra.Ring.Defs | {α : Type u_1} → [self : NonAssocRing α] → AddCommGroupWithOne α | true |
ContDiffWithinAt.contDiffBump | Mathlib.Analysis.Calculus.BumpFunction.Basic | ∀ {E : Type u_1} {X : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup X]
[inst_3 : NormedSpace ℝ X] [inst_4 : HasContDiffBump E] {n : ℕ∞} {c g : X → E} {s : Set X}
{f : (x : X) → ContDiffBump (c x)} {x : X},
ContDiffWithinAt ℝ (↑n) c s x →
ContDiffWithinAt ℝ (↑n... | true |
WithCStarModule.norm_apply_le_norm | Mathlib.Analysis.CStarAlgebra.Module.Constructions | ∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] {ι : Type u_2} {E : ι → Type u_3}
[inst_2 : Fintype ι] [inst_3 : (i : ι) → NormedAddCommGroup (E i)] [inst_4 : (i : ι) → Module ℂ (E i)]
[inst_5 : (i : ι) → SMul A (E i)] [inst_6 : (i : ι) → CStarModule A (E i)] [StarOrderedRing A]
(x : W... | true |
Nat.xor_right_injective | Batteries.Data.Nat.Bitwise | ∀ {x : ℕ}, Function.Injective fun x_1 => x ^^^ x_1 | true |
TopologicalSpace.le_def | Mathlib.Topology.Order | ∀ {α : Type u_1} {t s : TopologicalSpace α}, t ≤ s ↔ IsOpen ≤ IsOpen | true |
_private.Lean.Elab.Inductive.0.Lean.Elab.Command.elabCtors.match_7 | Lean.Elab.Inductive | (motive : Option Lean.FVarId → Sort u_1) →
(x : Option Lean.FVarId) →
((fvarId : Lean.FVarId) → motive (some fvarId)) → ((x : Option Lean.FVarId) → motive x) → motive x | false |
ValuationSubring.one_mem | Mathlib.RingTheory.Valuation.ValuationSubring | ∀ {K : Type u} [inst : Field K] (A : ValuationSubring K), 1 ∈ A | true |
TrivSqZeroExt.instAlgebra._proof_2 | Mathlib.Algebra.TrivSqZeroExt.Basic | ∀ (R' : Type u_1) (M : Type u_2) [inst : CommSemiring R'] [inst_1 : AddCommMonoid M] [inst_2 : Module R' M]
[inst_3 : Module R'ᵐᵒᵖ M] [IsCentralScalar R' M], IsScalarTower R' R'ᵐᵒᵖ M | false |
Lean.Elab.Command.InductiveElabStep3.finalize | Lean.Elab.MutualInductive | Lean.Elab.Command.InductiveElabStep3 → Lean.Elab.TermElabM Unit | true |
CategoryTheory.PullbackShift.adjunction | Mathlib.CategoryTheory.Shift.Pullback | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{A : Type u_2} →
{B : Type u_3} →
[inst_1 : AddMonoid A] →
[inst_2 : AddMonoid B] →
(φ : A →+ B) →
[inst_3 : CategoryTheory.HasShift C B] →
{D : Type u_4} →
[inst_4 ... | true |
MeasureTheory.SimpleFunc.ofIsEmpty._proof_1 | Mathlib.MeasureTheory.Function.SimpleFunc | ∀ {α : Type u_1} [IsEmpty α], Finite α | false |
Turing.TM0.Machine.map_step | Mathlib.Computability.TuringMachine.PostTuringMachine | ∀ {Γ : Type u_1} [inst : Inhabited Γ] {Γ' : Type u_2} [inst_1 : Inhabited Γ'] {Λ : Type u_3} [inst_2 : Inhabited Λ]
{Λ' : Type u_4} [inst_3 : Inhabited Λ'] (M : Turing.TM0.Machine Γ Λ) (f₁ : Turing.PointedMap Γ Γ')
(f₂ : Turing.PointedMap Γ' Γ) (g₁ : Λ → Λ') (g₂ : Λ' → Λ) {S : Set Λ},
Function.RightInverse f₁.f f... | true |
CategoryTheory.NatTrans.CommShift.verticalComposition | Mathlib.CategoryTheory.Shift.CommShift | ∀ {C₁ : Type u_1} {C₂ : Type u_2} {C₃ : Type u_3} {D₁ : Type u_4} {D₂ : Type u_5} {D₃ : Type u_6}
[inst : CategoryTheory.Category.{v_1, u_1} C₁] [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂]
[inst_2 : CategoryTheory.Category.{v_3, u_3} C₃] [inst_3 : CategoryTheory.Category.{v_4, u_4} D₁]
[inst_4 : CategoryTheo... | true |
CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.casesOn | 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 |
Lean.Json.instCoeArrayStructured | Lean.Data.Json.Basic | Coe (Array Lean.Json) Lean.Json.Structured | true |
groupCohomology.map_one_fst_of_isCocycle₂ | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | ∀ {G : Type u_1} {A : Type u_2} [inst : Monoid G] [inst_1 : AddCommGroup A] [inst_2 : MulAction G A] {f : G × G → A},
groupCohomology.IsCocycle₂ f → ∀ (g : G), f (1, g) = f (1, 1) | true |
_private.Mathlib.MeasureTheory.VectorMeasure.AddContent.0.MeasureTheory.VectorMeasure.exists_extension_of_isSetRing_of_le_measure_of_dense._simp_1_6 | Mathlib.MeasureTheory.VectorMeasure.AddContent | ∀ {α : Type u_1} {m : MeasurableSpace α} {s₁ s₂ : Set α},
MeasurableSet s₁ → MeasurableSet s₂ → MeasurableSet (s₁ ∪ s₂) = True | false |
Ordinal.iterate_veblen_lt_gamma_zero | Mathlib.SetTheory.Ordinal.Veblen | ∀ (n : ℕ), (fun a => Ordinal.veblen a 0)^[n] 0 < Ordinal.gamma 0 | true |
GaloisCoinsertion.isAtom_of_image | Mathlib.Order.Atoms | ∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : OrderBot α]
[inst_3 : OrderBot β] {l : α → β} {u : β → α} (gi : GaloisCoinsertion l u) {a : α}, IsAtom (l a) → IsAtom a | true |
Mathlib.Tactic.Widget.StringDiagram.Kind.monoidal.sizeOf_spec | Mathlib.Tactic.Widget.StringDiagram | sizeOf Mathlib.Tactic.Widget.StringDiagram.Kind.monoidal = 1 | true |
_private.Lean.Meta.Tactic.Contradiction.0.Lean.Meta.isGenDiseq | Lean.Meta.Tactic.Contradiction | Lean.Expr → Bool | true |
DifferentiableOn.sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {s : Set E},
DifferentiableOn ℝ f s → DifferentiableOn ℝ (fun x => Real.sinh (f x)) s | true |
Orientation.inner_smul_rotation_pi_div_two_smul_right | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | ∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
(o : Orientation ℝ V (Fin 2)) (x : V) (r₁ r₂ : ℝ), inner ℝ (r₂ • x) (r₁ • (o.rotation ↑(Real.pi / 2)) x) = 0 | true |
TopCat.Sheaf.interUnionPullbackCone._proof_3 | Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections | ∀ {X : TopCat} (U V : TopologicalSpace.Opens ↑X), U ⊓ V ≤ V | false |
Commute.zpow_right | Mathlib.Algebra.Group.Commute.Basic | ∀ {G : Type u_1} [inst : Group G] {a b : G}, Commute a b → ∀ (m : ℤ), Commute a (b ^ m) | true |
Filter.IsCobounded.mk | Mathlib.Order.Filter.IsBounded | ∀ {α : Type u_1} {r : α → α → Prop} {f : Filter α} [IsTrans α r] (a : α),
(∀ s ∈ f, ∃ x ∈ s, r a x) → Filter.IsCobounded r f | true |
SSet.stdSimplex.spineId | Mathlib.AlgebraicTopology.SimplicialSet.Path | (n : ℕ) → (SSet.stdSimplex.obj { len := n }).Path n | true |
Polynomial.Nontrivial.of_polynomial_ne | Mathlib.Algebra.Polynomial.Basic | ∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p ≠ q → Nontrivial R | true |
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 |
Array.Perm.pairwise | Init.Data.Array.Perm | ∀ {α : Type u_1} {R : α → α → Prop} {xs ys : Array α},
xs.Perm ys → List.Pairwise R xs.toList → (∀ {x y : α}, R x y → R y x) → List.Pairwise R ys.toList | 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] [IsOrderedRing 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✝) →
motive rest → motive (Lean.Meta.Grind.PendingSolverProp... | 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 |
List.allM._f | Init.Data.List.Control | {m : Type → Type u} → [Monad m] → {α : Type v} → (α → m Bool) → (x : List α) → List.below x → m Bool | 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 |
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 |
_private.Init.Data.String.Lemmas.Iterate.0.String.foldl.eq_1 | Init.Data.String.Lemmas.Iterate | ∀ {α : Type u} (f : α → Char → α) (init : α) (s : String), String.foldl f init s = String.Slice.foldl f init s.toSlice | true |
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