name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.42M | docString stringlengths 0 11k ⌀ | allowCompletion bool 2
classes |
|---|---|---|---|---|
_private.Mathlib.Util.AtomM.Recurse.0.Mathlib.Tactic.AtomM.Recurse.instBEqConfig.beq.match_1 | Mathlib.Util.AtomM.Recurse | (motive : Mathlib.Tactic.AtomM.Recurse.Config → Mathlib.Tactic.AtomM.Recurse.Config → Sort u_1) →
(x x_1 : Mathlib.Tactic.AtomM.Recurse.Config) →
((a : Lean.Meta.TransparencyMode) →
(a_1 a_2 : Bool) →
(b : Lean.Meta.TransparencyMode) →
(b_1 b_2 : Bool) →
motive { red :=... | null | false |
ContMDiffWithinAt.clm_postcomp | Mathlib.Geometry.Manifold.ContMDiff.NormedSpace | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {F₁ : Type u_8} [inst_6 : NormedAddComm... | null | true |
IsClub.isStationary | Mathlib.SetTheory.Cardinal.Cofinality.Club | ∀ {α : Type v} {s : Set α} [inst : LinearOrder α] [WellFoundedLT α] [Nonempty α],
Order.cof α ≠ Cardinal.aleph0 → IsClub s → IsStationary s | null | true |
_private.Mathlib.Geometry.Convex.Cone.Pointed.0.PointedCone.le_hull_singleton_iff._simp_1_1 | Mathlib.Geometry.Convex.Cone.Pointed | ∀ {A : Type u_1} {B : outParam (Type u_2)} {inst : Membership B A} {inst_1 : LE A} [self : IsConcreteLE A B] {S T : A},
(S ≤ T) = ∀ ⦃x : B⦄, x ∈ S → x ∈ T | null | false |
OrderMonoidHom.fst._proof_1 | Mathlib.Algebra.Order.Monoid.Lex | ∀ (α : Type u_1) (β : Type u_2) [inst : Monoid α] [inst_1 : PartialOrder α] [inst_2 : Monoid β] [inst_3 : Preorder β],
Monotone ⇑(MonoidHom.fst α β) | null | false |
OrderMonoidWithZeroHom._sizeOf_inst | Mathlib.Algebra.Order.Hom.MonoidWithZero | (α : Type u_6) →
(β : Type u_7) →
{inst : Preorder α} →
{inst_1 : Preorder β} →
{inst_2 : MulZeroOneClass α} → {inst_3 : MulZeroOneClass β} → [SizeOf α] → [SizeOf β] → SizeOf (α →*₀o β) | null | false |
SSet.N.mk_surjective | Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | ∀ {X : SSet} (x : X.N), ∃ n y, x = SSet.N.mk ↑y ⋯ | null | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Cell.Const.get?.match_1.splitter | Std.Data.DTreeMap.Internal.Model | {α : Type u_2} →
{β : Type u_1} →
(motive : Option ((_ : α) × β) → Sort u_3) →
(x : Option ((_ : α) × β)) → (Unit → motive none) → ((p : (_ : α) × β) → motive (some p)) → motive x | null | true |
Graph.IsEdgeCut.inter_edgeSet_of_le | Mathlib.Combinatorics.Graph.Connected.EdgeCut | ∀ {α : Type u_1} {β : Type u_2} {G H : Graph α β} {F : Set β}, H ≤ G → G.IsEdgeCut F → H.IsEdgeCut (H.edgeSet ∩ F) | null | true |
MeasureTheory.ae_mem_iff_measure_eq | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | ∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ] {s : Set α},
MeasureTheory.NullMeasurableSet s μ → ((∀ᵐ (a : α) ∂μ, a ∈ s) ↔ μ s = μ Set.univ) | null | true |
_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.zetaMul_prime_pow_nonneg._simp_1_2 | Mathlib.NumberTheory.LSeries.Nonvanishing | ∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} {n : ℕ} [IsReduced M₀] [Nontrivial M₀],
(a ^ n = 0) = (a = 0 ∧ n ≠ 0) | null | false |
Filter.mem_sup | Mathlib.Order.Filter.Basic | ∀ {α : Type u} {f g : Filter α} {s : Set α}, s ∈ f ⊔ g ↔ s ∈ f ∧ s ∈ g | null | true |
CategoryTheory.ShortComplex.leftHomologyFunctorOpNatIso._proof_1 | Mathlib.Algebra.Homology.ShortComplex.RightHomology | ∀ (C : Type u_1) [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
[inst_2 : CategoryTheory.Limits.HasKernels C] [inst_3 : CategoryTheory.Limits.HasCokernels C]
[inst_4 : CategoryTheory.Limits.HasKernels Cᵒᵖ] [inst_5 : CategoryTheory.Limits.HasCokernels Cᵒᵖ]
{X Y : ... | null | false |
AffineMap.instFunLike | Mathlib.LinearAlgebra.AffineSpace.AffineMap | (k : Type u_1) →
{V1 : Type u_2} →
(P1 : Type u_3) →
{V2 : Type u_4} →
(P2 : Type u_5) →
[inst : Ring k] →
[inst_1 : AddCommGroup V1] →
[inst_2 : Module k V1] →
[inst_3 : AddTorsor V1 P1] →
[inst_4 : AddCommGroup V2] →
... | null | true |
continuousAt_nsmul | Mathlib.Topology.Algebra.Monoid | ∀ {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : AddMonoid M] [ContinuousAdd M] (x : M) (n : ℕ),
ContinuousAt (fun x => n • x) x | null | true |
List.idxOf_cons_ne | Mathlib.Data.List.Basic | ∀ {α : Type u} [inst : BEq α] [LawfulBEq α] {a b : α} (l : List α),
b ≠ a → List.idxOf a (b :: l) = (List.idxOf a l).succ | null | true |
_private.Mathlib.RingTheory.Nullstellensatz.0.MvPolynomial.eq_vanishingIdeal_singleton_of_isMaximal._simp_1_1 | Mathlib.RingTheory.Nullstellensatz | ∀ {α : Type u} [inst : Semiring α] {I J : Ideal α}, (I = J) = ∀ (x : α), x ∈ I ↔ x ∈ J | null | false |
WeierstrassCurve.variableChange_a₂ | Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | ∀ {R : Type u} [inst : CommRing R] (W : WeierstrassCurve R) (C : WeierstrassCurve.VariableChange R),
(C • W).a₂ = ↑C.u⁻¹ ^ 2 * (W.a₂ - C.s * W.a₁ + 3 * C.r - C.s ^ 2) | null | true |
Lean.JsonRpc.MessageMetaData.response.elim | Lean.Data.JsonRpc | {motive : Lean.JsonRpc.MessageMetaData → Sort u} →
(t : Lean.JsonRpc.MessageMetaData) →
t.ctorIdx = 2 → ((id : Lean.JsonRpc.RequestID) → motive (Lean.JsonRpc.MessageMetaData.response id)) → motive t | null | false |
CategoryTheory.Limits.imageSubobject_arrow_comp | Mathlib.CategoryTheory.Subobject.Limits | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y)
[inst_1 : CategoryTheory.Limits.HasImage f],
CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImageSubobject f)
(CategoryTheory.Limits.imageSubobject f).arrow =
f | null | true |
RootPairing.EmbeddedG2.longRoot | Mathlib.LinearAlgebra.RootSystem.Finite.G2 | {ι : Type u_1} →
{R : Type u_2} →
{M : Type u_3} →
{N : Type u_4} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] →
[inst_2 : Module R M] →
[inst_3 : AddCommGroup N] → [inst_4 : Module R N] → (P : RootPairing ι R M N) → [P.EmbeddedG2] → M | The long root `β`. | true |
_private.Lean.Elab.Command.0.Lean.Elab.Command.runLinters.match_3 | Lean.Elab.Command | (motive : Option (IO.Promise Lean.Elab.InfoTree) → Sort u_1) →
(infoTreePromise? : Option (IO.Promise Lean.Elab.InfoTree)) →
((infoTreePromise : IO.Promise Lean.Elab.InfoTree) → motive (some infoTreePromise)) →
((x : Option (IO.Promise Lean.Elab.InfoTree)) → motive x) → motive infoTreePromise? | null | false |
Int.ediv_of_neg_of_pos | Mathlib.Data.Int.Init | ∀ {a b : ℤ}, a < 0 → 0 < b → a.ediv b = -((-a - 1) / b + 1) | null | true |
Complex.norm_natCast_cpow_of_pos | Mathlib.Analysis.SpecialFunctions.Pow.Real | ∀ {n : ℕ}, 0 < n → ∀ (s : ℂ), ‖↑n ^ s‖ = ↑n ^ s.re | null | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.TStructure.0.DerivedCategory.isGE_Q_obj_iff._simp_1_2 | Mathlib.Algebra.Homology.DerivedCategory.TStructure | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(K : CochainComplex C ℤ) (n : ℤ), K.IsGE n = ∀ i < n, HomologicalComplex.ExactAt K i | null | false |
PresheafOfModules.homMk._proof_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
{M₁ M₂ : PresheafOfModules R} (φ : M₁.presheaf ⟶ M₂.presheaf) (X : Cᵒᵖ) (x y : ↑(M₁.1 X)),
(CategoryTheory.ConcreteCategory.hom (φ.app X)) (x + y) =
(CategoryTheory.ConcreteCategory.hom (φ.app X)) x + (Catego... | null | false |
WType.brecOn | Mathlib.Data.W.Basic | {α : Type u_1} →
{β : α → Type u_2} →
{motive : WType β → Sort u} → (t : WType β) → ((t : WType β) → WType.below t → motive t) → motive t | null | false |
Char.any | Batteries.Data.Char.Basic | (Char → Bool) → Bool | Returns `true` if `p` returns true for some `Char`. | true |
IsScalarTower.of_compHom | Mathlib.Algebra.Algebra.Tower | ∀ (R : Type u) (A : Type w) (M : Type v₁) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : MulAction A M], IsScalarTower R A M | null | true |
OrthonormalBasis.repr_injective | Mathlib.Analysis.InnerProductSpace.PiL2 | ∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι], Function.Injective OrthonormalBasis.repr | null | true |
ShiftRight.recOn | Init.Prelude | {α : Type u} →
{motive : ShiftRight α → Sort u_1} →
(t : ShiftRight α) → ((shiftRight : α → α → α) → motive { shiftRight := shiftRight }) → motive t | null | false |
Matrix.transpose_hadamard | Mathlib.LinearAlgebra.Matrix.Hadamard | ∀ {α : Type u_1} {m : Type u_2} {n : Type u_3} [inst : Mul α] (A B : Matrix m n α),
(A.hadamard B).transpose = A.transpose.hadamard B.transpose | null | true |
CategoryTheory.ModObj.rec | Mathlib.CategoryTheory.Monoidal.Mod | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
{D : Type u₂} →
[inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
[inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] →
{M : C} →
[inst_4 : Cat... | null | false |
RingHom.closure_preimage_le | Mathlib.Algebra.Ring.Subring.Basic | ∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (f : R →+* S) (s : Set S),
Subring.closure (⇑f ⁻¹' s) ≤ Subring.comap f (Subring.closure s) | null | true |
Finset.add_subset_add_left | Mathlib.Algebra.Group.Pointwise.Finset.Basic | ∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Add α] {s t₁ t₂ : Finset α}, t₁ ⊆ t₂ → s + t₁ ⊆ s + t₂ | null | true |
Turing.TM1.stmts | Mathlib.Computability.TuringMachine.PostTuringMachine | {Γ : Type u_1} →
{Λ : Type u_2} → {σ : Type u_3} → (Λ → Turing.TM1.Stmt Γ Λ σ) → Finset Λ → Finset (Option (Turing.TM1.Stmt Γ Λ σ)) | The set of all statements in a Turing machine, plus one extra value `none` representing the
halt state. This is used in the TM1 to TM0 reduction. | true |
DiscreteUniformity.mk._flat_ctor | Mathlib.Topology.UniformSpace.DiscreteUniformity | ∀ {X : Type u_1} [u : UniformSpace X], u = ⊥ → DiscreteUniformity X | null | false |
FinPartOrd.dualEquiv_unitIso | Mathlib.Order.Category.FinPartOrd | FinPartOrd.dualEquiv.unitIso =
CategoryTheory.NatIso.ofComponents (fun X => FinPartOrd.Iso.mk (OrderIso.dualDual ↑X.toPartOrd))
@FinPartOrd.dualEquiv._proof_1 | null | true |
DifferentiableOn.inverse | Mathlib.Analysis.Calculus.FDeriv.Mul | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {R : Type u_4} [inst_3 : NormedRing R] [HasSummableGeomSeries R]
[inst_5 : NormedAlgebra 𝕜 R] {h : E → R} {S : Set E},
DifferentiableOn 𝕜 h S → (∀ x ∈ S, IsUnit (h x)) → Differentiabl... | null | true |
SymAlg.instNonAssocRingOfInvertibleOfNat._proof_14 | Mathlib.Algebra.Symmetrized | ∀ {α : Type u_1} [inst : Ring α] [inst_1 : Invertible 2] (a : αˢʸᵐ), a * 1 = a | null | false |
BddOrd.mk.injEq | Mathlib.Order.Category.BddOrd | ∀ (toPartOrd : PartOrd) [isBoundedOrder : BoundedOrder ↑toPartOrd] (toPartOrd_1 : PartOrd)
(isBoundedOrder_1 : BoundedOrder ↑toPartOrd_1),
({ toPartOrd := toPartOrd, isBoundedOrder := isBoundedOrder } =
{ toPartOrd := toPartOrd_1, isBoundedOrder := isBoundedOrder_1 }) =
(toPartOrd = toPartOrd_1 ∧ isBounde... | null | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.exists_linearIndepOn_extension.match_1_1 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | ∀ {ι : Type u_2} {V : Type u_1} {v : ι → V} {t : Set ι} (x : V) (motive : x ∈ v '' t → Prop) (x_1 : x ∈ v '' t),
(∀ (x_2 : ι) (hx : x_2 ∈ t) (hvx : v x_2 = x), motive ⋯) → motive x_1 | null | false |
QuadraticAlgebra.changeGeneratorEquiv.congr_simp | Mathlib.Algebra.QuadraticAlgebra.Discriminant | ∀ {R : Type u_2} [inst : CommRing R] (a b : R) (u u_1 : Rˣ) (e_u : u = u_1) (k k_1 : R) (e_k : k = k_1) {a' b' : R}
(ha : a' = ↑u ^ 2 * a - ↑u * b * k - k ^ 2) (hb : b' = ↑u * b + 2 * k),
QuadraticAlgebra.changeGeneratorEquiv a b u k ha hb = QuadraticAlgebra.changeGeneratorEquiv a b u_1 k_1 ⋯ ⋯ | null | true |
LinearMap.addMonoid._proof_3 | Mathlib.Algebra.Module.LinearMap.Defs | ∀ {R₁ : Type u_1} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : Semiring R₁] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M] [inst_5 : Module R₂ M₂]
{σ₁₂ : R₁ →+* R₂} (a : M →ₛₗ[σ₁₂] M₂), a + 0 = a | null | false |
BddLat.Iso.mk._proof_4 | Mathlib.Order.Category.BddLat | ∀ {α β : BddLat} (e : ↑α.toLat ≃o ↑β.toLat) (a b : ↑α.1), e (a ⊓ b) = e a ⊓ e b | null | false |
OneHom.comp_apply | Mathlib.Algebra.Group.Hom.Defs | ∀ {M : Type u_4} {N : Type u_5} {P : Type u_6} [inst : One M] [inst_1 : One N] [inst_2 : One P] (g : OneHom N P)
(f : OneHom M N) (x : M), (g.comp f) x = g (f x) | null | true |
Ideal.powQuotPowSuccLinearEquivMapMkPowSuccPow._proof_3 | Mathlib.RingTheory.Ideal.Quotient.Operations | ∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (n : ℕ), IsScalarTower R (R ⧸ I ^ (n + 1)) (R ⧸ I ^ (n + 1)) | null | false |
SimpleGraph.Copy.ext | Mathlib.Combinatorics.SimpleGraph.Copy | ∀ {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {H : SimpleGraph W} {f g : H.Copy G}, (∀ (a : W), f a = g a) → f = g | null | true |
BitVec.getElem?_zero_ofNat_zero | Init.Data.BitVec.Lemmas | ∀ {w : ℕ}, (0#(w + 1))[0]? = some false | null | true |
_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxi.Iterator.instIteratorLoop.loop.wf._unary._proof_2 | Init.Data.Range.Polymorphic.RangeIterator | ∀ {α : Type u_1} [inst : Std.PRange.UpwardEnumerable α] [Std.PRange.LawfulUpwardEnumerable α] (LargeEnough : α → Prop),
(∀ (a b : α), Std.PRange.UpwardEnumerable.LE a b → LargeEnough a → LargeEnough b) →
∀ (next : α), LargeEnough next → ∀ (next' : α), Std.PRange.succ? next = some next' → LargeEnough next' | null | false |
Filter.pureAddHom._proof_1 | Mathlib.Order.Filter.Pointwise | ∀ {α : Type u_1} [inst : Add α] (x x_1 : α), pure (x + x_1) = pure x + pure x_1 | null | false |
FreeMonoid.lift.eq_1 | Mathlib.Algebra.FreeMonoid.Basic | ∀ {α : Type u_1} {M : Type u_4} [inst : Monoid M],
FreeMonoid.lift =
{
toFun := fun f =>
{ toFun := fun l => FreeMonoid.prodAux (List.map f (FreeMonoid.toList l)), map_one' := ⋯, map_mul' := ⋯ },
invFun := fun f x => f (FreeMonoid.of x), left_inv := ⋯, right_inv := ⋯ } | null | true |
_private.Mathlib.Analysis.Normed.Module.Seminorm.Norm.0.closedBall_normSeminorm._simp_1_1 | Mathlib.Analysis.Normed.Module.Seminorm.Norm | ∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {x y : E} {r : ℝ}, (y ∈ p.closedBall x r) = (p (y - x) ≤ r) | null | false |
Finset.singleton_sdiv | Mathlib.Algebra.Group.Pointwise.Finset.Scalar | ∀ {α : Type u_1} {β : Type u_2} [inst : SDiv α β] [inst_1 : DecidableEq α] {t : Finset β} (a : β),
{a} /ₛ t = Finset.image (fun x => a /ₛ x) t | null | true |
VectorPrebundle.totalSpaceTopology | Mathlib.Topology.VectorBundle.Basic | {R : Type u_1} →
{B : Type u_2} →
{F : Type u_3} →
{E : B → Type u_4} →
[inst : NontriviallyNormedField R] →
[inst_1 : (x : B) → AddCommMonoid (E x)] →
[inst_2 : (x : B) → Module R (E x)] →
[inst_3 : NormedAddCommGroup F] →
[inst_4 : NormedSpace R ... | Topology on the total space that will make the prebundle into a bundle. | true |
PowerSeries.HasSubst | Mathlib.RingTheory.PowerSeries.Substitution | {τ : Type u_3} → {S : Type u_4} → [CommRing S] → MvPowerSeries τ S → Prop | (Possibly multivariate) power series which can be substituted in a `PowerSeries`. | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.0.UInt8.reduceBin.match_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.2231631932._hygCtx._hyg.9 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | (motive : Option UInt8 → Sort u_1) →
(__x : Option UInt8) → ((m : UInt8) → motive (some m)) → ((x : Option UInt8) → motive x) → motive __x | null | false |
LinearMap.FiniteRangeSetoid.setoid | Mathlib.Algebra.Module.LinearMap.FiniteRange | {K : Type u_1} →
{V : Type u_2} →
{V₂ : Type u_3} →
[inst : CommRing K] →
[inst_1 : AddCommGroup V] →
[inst_2 : Module K V] → [inst_3 : AddCommGroup V₂] → [inst_4 : Module K V₂] → Setoid (V →ₗ[K] V₂) | This is the equivalence relation on linear maps such that `u ≈ v` precisely
when `u - v` is a linear map with noetherian range. We allow ourself this slightly abusive name
because the more natural definition (`u - v` has finitely generated range) only yields a
well-behaved relation (more precisely, an additive congruen... | true |
WittVector.nsmul_coeff | Mathlib.RingTheory.WittVector.Defs | ∀ {p : ℕ} {R : Type u_1} [hp : Fact (Nat.Prime p)] [inst : CommRing R] (m : ℕ) (x : WittVector p R) (n : ℕ),
(m • x).coeff n = WittVector.peval (WittVector.wittNSMul p m n) ![x.coeff] | null | true |
MeasureTheory.instMetrizableSpaceProbabilityMeasure | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | ∀ (X : Type u_2) [inst : TopologicalSpace X] [TopologicalSpace.PseudoMetrizableSpace X]
[TopologicalSpace.SeparableSpace X] [inst_3 : MeasurableSpace X] [inst_4 : BorelSpace X],
TopologicalSpace.MetrizableSpace (MeasureTheory.ProbabilityMeasure X) | The topology of convergence in distribution on a separable Borel space is metrizable. | true |
Subgroup.IsSubnormal.recOn | Mathlib.GroupTheory.IsSubnormal | ∀ {G : Type u_1} [inst : Group G] {motive : (a : Subgroup G) → a.IsSubnormal → Prop} {a : Subgroup G}
(t : a.IsSubnormal),
motive ⊤ ⋯ →
(∀ (H K : Subgroup G) (h_le : H ≤ K) (hSubn : K.IsSubnormal) (hN : (H.subgroupOf K).Normal),
motive K hSubn → motive H ⋯) →
motive a t | null | false |
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom._default | Mathlib.CategoryTheory.Monoidal.Action.Basic | {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.MonoidalCategoryStruct C} →
(actionObj : C → D → D) →
({c c' : C} → (c ⟶ c') → (d : D) → actionObj c d ⟶ actionObj c' d) ... | null | false |
Lean.Lsp.instFileSourceSignatureHelpParams | Lean.Server.FileSource | Lean.Lsp.FileSource Lean.Lsp.SignatureHelpParams | null | true |
_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat | Mathlib.Computability.TuringDegree | Preorder (ℕ →. ℕ) | null | true |
Lean.IR.Checker.markIndex | Lean.Compiler.IR.Checker | Lean.IR.Index → Lean.IR.Checker.M Unit | null | true |
Option.filter_some | Init.Data.Option.Lemmas | ∀ {α : Type u_1} {p : α → Bool} {a : α}, Option.filter p (some a) = if p a = true then some a else none | null | true |
_private.Mathlib.Algebra.Ring.Int.Parity.0.Int.sq_emod_four._proof_1_1 | Mathlib.Algebra.Ring.Int.Parity | ∀ (k : ℤ), (2 * k) ^ 2 % 4 = 2 * k % 2 | null | false |
MvPowerSeries.instInv | Mathlib.RingTheory.MvPowerSeries.Inverse | {σ : Type u_1} → {k : Type u_3} → [Field k] → Inv (MvPowerSeries σ k) | null | true |
Lean.Elab.Tactic.closeMainGoal | Lean.Elab.Tactic.Basic | Lean.Name → Lean.Expr → optParam Bool true → Lean.Elab.Tactic.TacticM Unit | Closes main goal using the given expression.
If `checkUnassigned == true`, then `val` must not contain unassigned metavariables.
Returns `true` if `val` was successfully used to close the goal.
| true |
Lean.Elab.GoalsAtResult | Lean.Elab.InfoTree.Util | Type | null | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_2 | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | ∀ {α : Type u} {P : List α → Prop}, (∃ l, P l) = ∃ n f, P (List.ofFn f) | null | false |
FirstOrder.Language.BoundedFormula.all_iff_not_ex_not | Mathlib.ModelTheory.Equivalence | ∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} (φ : L.BoundedFormula α (n + 1)),
T.Iff φ.all φ.not.ex.not | null | true |
Lean.Lsp.instToJsonChangeAnnotation.toJson | Lean.Data.Lsp.Basic | Lean.Lsp.ChangeAnnotation → Lean.Json | null | true |
Lean.Lsp.instFromJsonCallHierarchyPrepareParams.fromJson | Lean.Data.Lsp.LanguageFeatures | Lean.Json → Except String Lean.Lsp.CallHierarchyPrepareParams | null | true |
HomologicalComplex.homotopyCofiber.XIsoBiprod.congr_simp | Mathlib.Algebra.Homology.HomotopyCofiber | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_2}
{c : ComplexShape ι} {F G : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
[inst_3 : DecidableRel c.Rel] (i j : ι) (hij : c.Rel i j)
[inst_4 : CategoryTheor... | null | true |
AntitoneOn.Ico | Mathlib.Order.Interval.Set.Monotone | ∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f g : α → β} {s : Set α},
AntitoneOn f s → MonotoneOn g s → MonotoneOn (fun x => Set.Ico (f x) (g x)) s | null | true |
List.reduceOption_cons_of_some | Mathlib.Data.List.ReduceOption | ∀ {α : Type u_1} (x : α) (l : List (Option α)), (some x :: l).reduceOption = x :: l.reduceOption | null | true |
Ordinal.invVeblen₂_gamma | Mathlib.SetTheory.Ordinal.Veblen | ∀ (o : Ordinal.{u_1}), o.gamma.invVeblen₂ = 0 | null | true |
IsJordan.mk._flat_ctor | Mathlib.Algebra.Jordan.Basic | ∀ {A : Type u_1} [inst : Mul A],
(∀ (a b : A), a * b * a = a * (b * a)) →
(∀ (a b : A), a * a * (a * b) = a * (a * a * b)) →
(∀ (a b : A), a * a * (b * a) = a * a * b * a) →
(∀ (a b : A), a * b * (a * a) = a * (b * (a * a))) →
(∀ (a b : A), b * a * (a * a) = b * (a * a) * a) → IsJordan A | null | false |
_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_2 | Mathlib.Data.Nat.ChineseRemainder | ∀ {k : ℕ} {l : List ℕ}, k.Coprime l.prod = ∀ n ∈ l, k.Coprime n | null | false |
_private.Mathlib.RingTheory.Coalgebra.GroupLike.0.isGroupLikeElem_self._simp_1_1 | Mathlib.RingTheory.Coalgebra.GroupLike | ∀ (R : Type u_2) {A : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
[inst_3 : Coalgebra R A] (a : A),
IsGroupLikeElem R a = (CoalgebraStruct.counit a = 1 ∧ CoalgebraStruct.comul a = a ⊗ₜ[R] a) | null | false |
MeasureTheory.average_smul_const | Mathlib.MeasureTheory.Integral.Average | ∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
(μ : MeasureTheory.Measure α) {𝕜 : Type u_4} [inst_2 : RCLike 𝕜] [inst_3 : NormedSpace 𝕜 E] [CompleteSpace E]
(f : α → 𝕜) (c : E), ⨍ (a : α), f a • c ∂μ = (⨍ (a : α), f a ∂μ) • c | null | true |
Combinatorics.Line._sizeOf_inst | Mathlib.Combinatorics.HalesJewett | (α : Type u_5) → (ι : Type u_6) → [SizeOf α] → [SizeOf ι] → SizeOf (Combinatorics.Line α ι) | null | false |
Mathlib.Meta.NormNum.isInt_lcm | Mathlib.Tactic.NormNum.GCD | ∀ {x y nx ny : ℤ} {z : ℕ},
Mathlib.Meta.NormNum.IsInt x nx →
Mathlib.Meta.NormNum.IsInt y ny → nx.lcm ny = z → Mathlib.Meta.NormNum.IsNat (x.lcm y) z | null | true |
ZeroAtInftyContinuousMap.unitizationEquiv._proof_1 | Mathlib.Topology.ContinuousMap.ZeroAtInftyUnitization | ∀ (X : Type u_2) (R : Type u_1) [inst : TopologicalSpace X] [inst_1 : R1Space X] [inst_2 : TopologicalSpace R]
[inst_3 : AddCommGroup R] [inst_4 : IsTopologicalAddGroup R] (f : Unitization R (ZeroAtInftyContinuousMap X R)),
Unitization.mk
((ContinuousMap.const (OnePoint X) f.toProd.1 + f.toProd.2.toOnePoint) ... | null | false |
iSup_subtype' | Mathlib.Order.CompleteLattice.Basic | ∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {p : ι → Prop} {f : (i : ι) → p i → α},
⨆ i, ⨆ (h : p i), f i h = ⨆ x, f ↑x ⋯ | null | true |
BitVec.msb_twoPow | Init.Data.BitVec.Lemmas | ∀ {i w : ℕ}, (BitVec.twoPow w i).msb = (decide (i < w) && decide (i = w - 1)) | null | true |
GrpCat.SurjectiveOfEpiAuxs.tau._proof_1 | Mathlib.Algebra.Category.Grp.EpiMono | ∀ {A B : GrpCat} (f : A ⟶ B), ∃ y, y • ↑(GrpCat.Hom.hom f).range = ↑(GrpCat.Hom.hom f).range | null | false |
MulAction.isPreprimitive_stabilizer_of_surjective | Mathlib.GroupTheory.Perm.MaximalSubgroups | ∀ {M : Type u_1} {α : Type u_2} [inst : Group M] [inst_1 : MulAction M α] (s : Set α),
Function.Surjective MulAction.toPerm → MulAction.IsPreprimitive ↥(MulAction.stabilizer M s) ↑s | In the permutation group, the stabilizer of any set
acts primitively on that set. | true |
HomologicalComplex.dFrom_eq | Mathlib.Algebra.Homology.HomologicalComplex | ∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} (C : HomologicalComplex V c) {i j : ι}
(r : c.Rel i j), C.dFrom i = CategoryTheory.CategoryStruct.comp (C.d i j) (C.xNextIso r).inv | null | true |
Lean.Widget.RpcEncodablePacket.«_@».Lean.Widget.UserWidget.577854155._hygCtx._hyg.1.recOn | Lean.Widget.UserWidget | {motive : Lean.Widget.RpcEncodablePacket✝ → Sort u} →
(t : Lean.Widget.RpcEncodablePacket✝) → ((widgets : Lean.Json) → motive { widgets := widgets }) → motive t | null | false |
_private.Mathlib.ModelTheory.Semantics.0.FirstOrder.Language.model_distinctConstantsTheory._simp_1_1 | Mathlib.ModelTheory.Semantics | ∀ {α : Type u} {β : Type v} (f : α → β) (s : Set α) (y : β), (y ∈ f '' s) = ∃ x ∈ s, f x = y | null | false |
Ordinal.omega | Mathlib.SetTheory.Cardinal.Aleph | Ordinal.{u_1} ↪o Ordinal.{u_1} | The `omega` function gives the infinite initial ordinals listed by their ordinal index.
`omega 0 = ω`, `omega 1 = ω₁` is the first uncountable ordinal, and so on.
This is not to be confused with the first infinite ordinal `Ordinal.omega0`.
For a version including finite ordinals, see `Ordinal.preOmega`.
Conventions... | true |
AddChar.circleEquivComplex._proof_5 | Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality | ∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : Finite α] (ψ : AddChar α ℂ),
(fun ψ => AddChar.toMonoidHomEquiv.symm (Circle.coeHom.comp ψ.toMonoidHom))
((fun ψ => { toFun := fun a => ⟨ψ a, ⋯⟩, map_zero_eq_one' := ⋯, map_add_eq_mul' := ⋯ }) ψ) =
ψ | null | false |
Batteries.Tactic.Lint.isAutoDecl | Batteries.Tactic.Lint.Basic | {m : Type → Type} → [Monad m] → [Lean.MonadEnv m] → Lean.Name → m Bool | Returns true if `decl` is an automatically generated declaration.
Also returns true if `decl` is an internal name or created during macro
expansion.
See `Lean.Environment.isAutoDecl` for an identical pure version of this function on the environment.
| true |
CategoryTheory.Mon.tensorUnit_mul | Mathlib.CategoryTheory.Monoidal.Mon | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.BraidedCategory C],
CategoryTheory.MonObj.mul =
(CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).hom | null | true |
_private.Lean.Parser.Term.0.Lean.Parser.Term.proj._regBuiltin.Lean.Parser.Term.proj_1 | Lean.Parser.Term | IO Unit | null | false |
_private.Mathlib.MeasureTheory.Integral.SetToL1.ChangeMeasure.0.MeasureTheory.setToFun_top_smul_measure._simp_1_3 | Mathlib.MeasureTheory.Integral.SetToL1.ChangeMeasure | (¬False) = True | null | false |
DirectLimit.instMulDistribMulActionOfMulActionHomClass._proof_4 | Mathlib.Algebra.Colimit.DirectLimit | ∀ {R : Type u_4} {ι : Type u_1} [inst : Preorder ι] {G : ι → Type u_2} {T : ⦃i j : ι⦄ → i ≤ j → Type u_3}
{f : (x x_1 : ι) → (h : x ≤ x_1) → T h} [inst_1 : (i j : ι) → (h : i ≤ j) → FunLike (T h) (G i) (G j)]
[inst_2 : DirectedSystem G fun x1 x2 x3 => ⇑(f x1 x2 x3)] [inst_3 : IsDirectedOrder ι] [inst_4 : Nonempty ι... | null | false |
HasMFDerivWithinAt._proof_2 | Mathlib.Geometry.Manifold.MFDeriv.Defs | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜], RingHomInvPair (RingHom.id 𝕜) (RingHom.id 𝕜) | null | false |
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