name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
Vector.finIdxOf?_mk | Init.Data.Vector.Lemmas | ∀ {α : Type u_1} {n : ℕ} [inst : BEq α] {xs : Array α} (h : xs.size = n) (x : α),
(Vector.mk xs h).finIdxOf? x = Option.map (Fin.cast h) (xs.finIdxOf? x) | true |
Finset.toRight | Mathlib.Data.Finset.Sum | {α : Type u_1} → {β : Type u_2} → Finset (α ⊕ β) → Finset β | true |
DirectedOn.le_of_minimal | Mathlib.Order.Bounds.Basic | ∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a b : α},
DirectedOn (fun x y => y ≤ x) s → Minimal (fun x => x ∈ s) a → b ∈ s → a ≤ b | true |
WittVector.instIsocrystalStandardOneDimIsocrystal._proof_2 | Mathlib.RingTheory.WittVector.Isocrystal | ∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (k : Type u_1) [inst_1 : CommRing k] [inst_2 : CharP k p]
[inst_3 : PerfectRing k p],
RingHomCompTriple (↑(WittVector.FractionRing.frobenius p k)) (RingHom.id (FractionRing (WittVector p k)))
↑(WittVector.FractionRing.frobenius p k) | false |
Sum.instLocallyFiniteOrder._proof_1 | Mathlib.Data.Sum.Interval | ∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : LocallyFiniteOrder α]
[inst_3 : LocallyFiniteOrder β] (a b x : α ⊕ β), x ∈ Finset.sumLift₂ Finset.Icc Finset.Icc a b ↔ a ≤ x ∧ x ≤ b | false |
CanonicallyOrderedAddCommMonoid.toAddCancelCommMonoid | Mathlib.Algebra.Order.Sub.Basic | (α : Type u_1) →
[inst : AddCommMonoid α] →
[inst_1 : PartialOrder α] → [inst_2 : Sub α] → [OrderedSub α] → [AddLeftReflectLE α] → AddCancelCommMonoid α | true |
Submodule.rank_sup_add_rank_inf_eq | Mathlib.LinearAlgebra.Dimension.RankNullity | ∀ {R : Type u_1} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[HasRankNullity.{u, u_1} R] (s t : Submodule R M),
Module.rank R ↥(s ⊔ t) + Module.rank R ↥(s ⊓ t) = Module.rank R ↥s + Module.rank R ↥t | true |
comp_partialSups | Mathlib.Order.PartialSups | ∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : SemilatticeSup β]
[inst_2 : Preorder ι] [inst_3 : LocallyFiniteOrderBot ι] {F : Type u_4} [inst_4 : FunLike F α β] [SupHomClass F α β]
(f : ι → α) (g : F), ⇑(partialSups (⇑g ∘ f)) = ⇑g ∘ ⇑(partialSups f) | true |
Module.End.UnifEigenvalues.val | Mathlib.LinearAlgebra.Eigenspace.Basic | {R : Type v} →
{M : Type w} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (f : Module.End R M) → (k : ℕ∞) → f.UnifEigenvalues k → R | true |
_private.Mathlib.Topology.MetricSpace.Thickening.0.Metric.thickening_eq_empty_iff._simp_1_1 | Mathlib.Topology.MetricSpace.Thickening | ∀ {α : Type u} [inst : PseudoEMetricSpace α] {ε : ℝ} {s : Set α}, 0 < ε → (Metric.thickening ε s = ∅) = (s = ∅) | false |
CategoryTheory.GradedObject.mapBifunctorLeftUnitor_naturality | Mathlib.CategoryTheory.GradedObject.Unitor | ∀ {C : Type u_1} {D : Type u_2} {I : Type u_3} {J : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : Zero I] [inst_3 : DecidableEq I]
[inst_4 : CategoryTheory.Limits.HasInitial C] (F : CategoryTheory.Functor C (CategoryTheory.Functor D D)) (X : C)
(... | true |
Finset.addConst_neg_left | Mathlib.Combinatorics.Additive.DoublingConst | ∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : DecidableEq G] (A B : Finset G), (-A).addConst B = A.subConst B | true |
CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback._proof_7 | Mathlib.CategoryTheory.MorphismProperty.OverAdjunction | ∀ {T : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} T] {P : CategoryTheory.MorphismProperty T} {Y Z : T}
(g : Y ⟶ Z) [CategoryTheory.Limits.HasPullbacks T], P.HasPullbacksAlong g | false |
Congr!.Config._sizeOf_1 | Mathlib.Tactic.CongrExclamation | Congr!.Config → ℕ | false |
Std.DHashMap.Internal.Raw₀.toList_map | Std.Data.DHashMap.Internal.RawLemmas | ∀ {α : Type u} {β : α → Type v} {γ : α → Type w} (m : Std.DHashMap.Internal.Raw₀ α β) {f : (a : α) → β a → γ a},
(↑(Std.DHashMap.Internal.Raw₀.map f m)).toList.Perm (List.map (fun p => ⟨p.fst, f p.fst p.snd⟩) (↑m).toList) | true |
Turing.TM2to1.StAct.rec | Mathlib.Computability.TuringMachine.StackTuringMachine | {K : Type u_1} →
{Γ : K → Type u_2} →
{σ : Type u_4} →
{k : K} →
{motive : Turing.TM2to1.StAct K Γ σ k → Sort u} →
((a : σ → Γ k) → motive (Turing.TM2to1.StAct.push a)) →
((a : σ → Option (Γ k) → σ) → motive (Turing.TM2to1.StAct.peek a)) →
((a : σ → Option (Γ k) →... | false |
CategoryTheory.Functor.CoconeTypes.IsColimit.fac_apply | Mathlib.CategoryTheory.Limits.Types.ColimitType | ∀ {J : Type u} [inst : CategoryTheory.Category.{v, u} J] {F : CategoryTheory.Functor J (Type w₀)} {c : F.CoconeTypes}
(hc : c.IsColimit) (c' : F.CoconeTypes) (j : J) (x : F.obj j), hc.desc c' (c.ι j x) = c'.ι j x | true |
Lean.Parser.doElemParser | Lean.Parser.Do | optParam ℕ 0 → Lean.Parser.Parser | true |
HasDerivAt.comp_sub_const | Mathlib.Analysis.Calculus.Deriv.Shift | ∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} (x a : 𝕜),
HasDerivAt f f' (x - a) → HasDerivAt (fun x => f (x - a)) f' x | true |
NumberField.logHeight₁_eq | Mathlib.NumberTheory.Height.NumberField | ∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : K),
Height.logHeight₁ x = ∑ v, ↑v.mult * (v x).posLog + ∑ᶠ (v : NumberField.FinitePlace K), (v x).posLog | true |
Aesop.Script.StepTree.toMessageData | Aesop.Script.UScriptToSScript | Aesop.Script.StepTree → Lean.MessageData | true |
IsFiniteLength.of_subsingleton._simp_1 | Mathlib.RingTheory.FiniteLength | ∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Subsingleton M],
IsFiniteLength R M = True | false |
MeasureTheory.Measure.MutuallySingular.zero_left | Mathlib.MeasureTheory.Measure.MutuallySingular | ∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}, MeasureTheory.Measure.MutuallySingular 0 μ | true |
Module.Basis.extendLe_subset | Mathlib.LinearAlgebra.Basis.VectorSpace | ∀ {K : Type u_3} {V : Type u_4} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s t : Set V}
(hs : LinearIndepOn K id s) (hst : s ⊆ t) (ht : ⊤ ≤ Submodule.span K t),
Set.range ⇑(Module.Basis.extendLe hs hst ht) ⊆ t | true |
Lean.HeadIndex.lam.sizeOf_spec | Lean.HeadIndex | sizeOf Lean.HeadIndex.lam = 1 | true |
_private.Mathlib.Analysis.Normed.Group.Basic.0.nontrivialTopology_iff_exists_nnnorm_ne_zero'._simp_1_2 | Mathlib.Analysis.Normed.Group.Basic | ∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α}, Inseparable x y = (nndist x y = 0) | false |
LinearIsometryEquiv.conjStarAlgEquiv._proof_2 | Mathlib.Analysis.InnerProductSpace.Adjoint | ∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {H : Type u_2} [inst_1 : NormedAddCommGroup H] [inst_2 : InnerProductSpace 𝕜 H],
SMulCommClass 𝕜 𝕜 H | false |
Std.Internal.List.minKey?_eq_some_minKey | 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)} {he : l.isEmpty = false},
Std.Internal.List.minKey? l = some (Std.Internal.List.minKey l he) | true |
IsOrderedVAdd.vadd_le_vadd_right | Mathlib.Algebra.Order.AddTorsor | ∀ {G : Type u_3} {P : Type u_4} {inst : LE G} {inst_1 : LE P} {inst_2 : VAdd G P} [self : IsOrderedVAdd G P] (c d : G),
c ≤ d → ∀ (a : P), c +ᵥ a ≤ d +ᵥ a | true |
_private.Mathlib.RingTheory.DedekindDomain.Different.0.FractionalIdeal.trace_mem_dual_one._simp_1_2 | Mathlib.RingTheory.DedekindDomain.Different | ∀ {A : Type u_1} {K : Type u_2} {L : Type u} {B : Type u_3} [inst : CommRing A] [inst_1 : Field K] [inst_2 : CommRing B]
[inst_3 : Field L] [inst_4 : Algebra A K] [inst_5 : Algebra B L] [inst_6 : Algebra A B] [inst_7 : Algebra K L]
[inst_8 : Algebra A L] [inst_9 : IsScalarTower A K L] [inst_10 : IsScalarTower A B L... | false |
Std.IteratorLoop.WithWF.mk._flat_ctor | Init.Data.Iterators.Consumers.Monadic.Loop | {α : Type w} →
{m : Type w → Type w'} →
{β : Type w} →
[inst : Std.Iterator α m β] →
{γ : Type x} →
{PlausibleForInStep : β → γ → ForInStep γ → Prop} →
{hwf : Std.IteratorLoop.WellFounded α m PlausibleForInStep} →
Std.IterM m β → γ → Std.IteratorLoop.WithWF α m Pl... | false |
RelIso.eq_iff_eq | Mathlib.Order.RelIso.Basic | ∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (f : r ≃r s) {a b : α}, f a = f b ↔ a = b | true |
CStarModule.innerₛₗ._proof_4 | Mathlib.Analysis.CStarAlgebra.Module.Defs | ∀ {A : Type u_1} {E : Type u_2} [inst : NonUnitalRing A] [inst_1 : StarRing A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ A] [inst_4 : Module ℂ E] [inst_5 : PartialOrder A] [inst_6 : SMul A E] [inst_7 : Norm A]
[inst_8 : Norm E] [inst_9 : CStarModule A E] [StarModule ℂ A] (z : ℂ) (y : E),
{ toFun := fun y_1 => ... | false |
Qq.instBEqQuoted._aux_1 | Qq.Typ | failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation) | false |
Batteries.RBNode.Balanced.del | Batteries.Data.RBMap.WF | ∀ {α : Type u_1} {c : Batteries.RBColor} {n : ℕ} {cut : α → Ordering} {t : Batteries.RBNode α},
t.Balanced c n → Batteries.RBNode.DelProp t.isBlack (Batteries.RBNode.del cut t) n | true |
Fin.insertNth_sub | Mathlib.Algebra.Group.Fin.Tuple | ∀ {n : ℕ} {α : Fin (n + 1) → Type u_1} [inst : (j : Fin (n + 1)) → Sub (α j)] (i : Fin (n + 1)) (x y : α i)
(p q : (j : Fin n) → α (i.succAbove j)), i.insertNth (x - y) (p - q) = i.insertNth x p - i.insertNth y q | true |
Quaternion.imK_ratCast | Mathlib.Algebra.Quaternion | ∀ {R : Type u_1} [inst : Field R] (q : ℚ), (↑q).imK = 0 | true |
_private.Qq.AssertInstancesCommute.0.Qq.Impl._aux_Qq_AssertInstancesCommute___elabRules_Qq_Impl_termAssertInstancesCommuteImpl__1.match_1 | Qq.AssertInstancesCommute | (motive :
Option (Lean.FVarId × (u : Q(Lean.Level)) × (ty : Q(Q(Sort «$u»))) × Q(Q(«$$ty»)) × Q(Q(«$$ty»))) → Sort u_1) →
(__do_lift : Option (Lean.FVarId × (u : Q(Lean.Level)) × (ty : Q(Q(Sort «$u»))) × Q(Q(«$$ty»)) × Q(Q(«$$ty»)))) →
((fvar : Lean.FVarId) →
(fst : Q(Lean.Level)) →
(fst_1 :... | false |
_private.Mathlib.Topology.DiscreteSubset.0.mem_codiscreteWithin._simp_1_5 | Mathlib.Topology.DiscreteSubset | ∀ {α : Type u} {s t : Set α} (x : α), (x ∈ s \ t) = (x ∈ s ∧ x ∉ t) | false |
OrderAddMonoidHom.fst_apply | Mathlib.Algebra.Order.Monoid.Lex | ∀ (α : Type u_1) (β : Type u_2) [inst : AddMonoid α] [inst_1 : PartialOrder α] [inst_2 : AddMonoid β]
[inst_3 : Preorder β] (self : α × β), (OrderAddMonoidHom.fst α β) self = self.1 | true |
QuotientAddGroup.homQuotientZSMulOfHom_comp | Mathlib.GroupTheory.QuotientGroup.Basic | ∀ {A B : Type u} [inst : AddCommGroup A] [inst_1 : AddCommGroup B] (f : A →+ B) (g : B →+ A) (n : ℤ),
QuotientAddGroup.homQuotientZSMulOfHom (f.comp g) n =
(QuotientAddGroup.homQuotientZSMulOfHom f n).comp (QuotientAddGroup.homQuotientZSMulOfHom g n) | true |
CategoryTheory.yonedaJointlyReflectsLimits._proof_1 | Mathlib.CategoryTheory.Limits.Yoneda | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {J : Type u_4}
[inst_1 : CategoryTheory.Category.{u_3, u_4} J] (F : CategoryTheory.Functor J Cᵒᵖ) (c : CategoryTheory.Limits.Cone F)
(hc : (X : C) → CategoryTheory.Limits.IsLimit ((CategoryTheory.yoneda.obj X).mapCone c))
(s : CategoryTheory.Limits.Co... | false |
CategoryTheory.Limits.createsLimitsOfShapeOfCreatesEqualizersAndProducts._proof_3 | Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {J : Type u_1} [inst_1 : CategoryTheory.SmallCategory J]
{K : CategoryTheory.Functor J C},
CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete J) C →
CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete ((p : J × J) × (p.1 ⟶ p... | false |
CommAlgCat.algEquivOfIso_apply | Mathlib.Algebra.Category.CommAlgCat.Basic | ∀ {R : Type u} [inst : CommRing R] {A B : CommAlgCat R} (i : A ≅ B) (a : ↑A),
(CommAlgCat.algEquivOfIso i) a = (CategoryTheory.ConcreteCategory.hom i.hom) a | true |
Aesop.TreeRef.rec | Aesop.Tree.Traversal | {motive : Aesop.TreeRef → Sort u} →
((gref : Aesop.GoalRef) → motive (Aesop.TreeRef.goal gref)) →
((rref : Aesop.RappRef) → motive (Aesop.TreeRef.rapp rref)) →
((cref : Aesop.MVarClusterRef) → motive (Aesop.TreeRef.mvarCluster cref)) → (t : Aesop.TreeRef) → motive t | false |
div_ne_one | Mathlib.Algebra.Group.Basic | ∀ {G : Type u_3} [inst : Group G] {a b : G}, a / b ≠ 1 ↔ a ≠ b | true |
ENat.instUniqueUnits | Mathlib.Data.ENat.Basic | Unique ℕ∞ˣ | true |
ContinuousMultilinearMap.linearDeriv.congr_simp | Mathlib.Analysis.Normed.Module.Multilinear.Basic | ∀ {R : Type u} {ι : Type v} {M₁ : ι → Type w₁} {M₂ : Type w₂} [inst : Semiring 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] [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] [inst_6 : TopologicalSpace M₂]
(f f_1 : ContinuousMultili... | true |
Subsemigroup.op._proof_1 | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | ∀ {M : Type u_1} [inst : Mul M] (x : Subsemigroup M) {a b : Mᵐᵒᵖ},
a ∈ MulOpposite.unop ⁻¹' ↑x → b ∈ MulOpposite.unop ⁻¹' ↑x → MulOpposite.unop b * MulOpposite.unop a ∈ x | false |
CategoryTheory.Bicategory.Prod.sectL._proof_8 | Mathlib.CategoryTheory.Bicategory.Product | ∀ (B : Type u_2) [inst : CategoryTheory.Bicategory B] {C : Type u_6} [inst_1 : CategoryTheory.Bicategory C] (c : C)
{a b c_1 : B} {f g : a ⟶ b} (η : f ⟶ g) (h : b ⟶ c_1),
CategoryTheory.Prod.mkHom (CategoryTheory.Bicategory.whiskerRight η h)
(CategoryTheory.CategoryStruct.id (CategoryTheory.CategoryStruct.id ... | false |
FirstOrder.Language.presburger.funMap_one | Mathlib.ModelTheory.Arithmetic.Presburger.Basic | ∀ {M : Type u_2} [inst : Zero M] [inst_1 : One M] [inst_2 : Add M] {v : Fin 0 → M},
FirstOrder.Language.Structure.funMap FirstOrder.presburgerFunc.one v = 1 | true |
TopologicalSpace.prod_mono | Mathlib.Topology.Constructions.SumProd | ∀ {α : Type u_5} {β : Type u_6} {σ₁ σ₂ : TopologicalSpace α} {τ₁ τ₂ : TopologicalSpace β},
σ₁ ≤ σ₂ → τ₁ ≤ τ₂ → instTopologicalSpaceProd ≤ instTopologicalSpaceProd | true |
_private.Batteries.Data.MLList.Basic.0.MLList.Spec.mk.sizeOf_spec | Batteries.Data.MLList.Basic | ∀ {m : Type u → Type u} [inst : (a : Type u) → SizeOf (m a)] (listM : Type u → Type u) (nil : {α : Type u} → listM α)
(cons : {α : Type u} → α → listM α → listM α) (thunk : {α : Type u} → (Unit → listM α) → listM α)
(squash : {α : Type u} → (Unit → m (listM α)) → listM α)
(uncons : {α : Type u} → [Monad m] → list... | true |
coe_iterateFrobeniusEquiv | Mathlib.FieldTheory.Perfect | ∀ (R : Type u_1) (p n : ℕ) [inst : CommSemiring R] [inst_1 : ExpChar R p] [inst_2 : PerfectRing R p],
⇑(iterateFrobeniusEquiv R p n) = ⇑(iterateFrobenius R p n) | true |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded.incMod | Std.Sync.Channel | ℕ → ℕ → ℕ | true |
Flow.cont' | Mathlib.Dynamics.Flow | ∀ {τ : Type u_1} [inst : TopologicalSpace τ] [inst_1 : AddMonoid τ] [inst_2 : ContinuousAdd τ] {α : Type u_2}
[inst_3 : TopologicalSpace α] (self : Flow τ α), Continuous (Function.uncurry self.toFun) | true |
Turing.Dir.ofNat_ctorIdx | Mathlib.Computability.TuringMachine.Tape | ∀ (x : Turing.Dir), Turing.Dir.ofNat x.ctorIdx = x | true |
_private.Mathlib.FieldTheory.Differential.Basic.0.Differential.logDeriv_div._simp_1_7 | Mathlib.FieldTheory.Differential.Basic | ∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R] (n : ℕ), (↑n + 1 = 0) = False | false |
_private.Lean.Elab.Tactic.Try.0.Lean.Elab.Tactic.Try.isAccessible._sparseCasesOn_1.else_eq | Lean.Elab.Tactic.Try | ∀ {α : Type u} {motive : Option α → Sort u_1} (t : Option α) (some : (val : α) → motive (some val))
(«else» : Nat.hasNotBit 2 t.ctorIdx → motive t) (h : Nat.hasNotBit 2 t.ctorIdx),
Lean.Elab.Tactic.Try.isAccessible._sparseCasesOn_1✝ t some «else» = «else» h | false |
Filter.prod_map_map_eq' | Mathlib.Order.Filter.Prod | ∀ {α₁ : Type u_6} {α₂ : Type u_7} {β₁ : Type u_8} {β₂ : Type u_9} (f : α₁ → α₂) (g : β₁ → β₂) (F : Filter α₁)
(G : Filter β₁), Filter.map f F ×ˢ Filter.map g G = Filter.map (Prod.map f g) (F ×ˢ G) | true |
_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.iInf_ker_lapply_le_bot._simp_1_4 | Mathlib.LinearAlgebra.Finsupp.Span | ∀ (R : Type u_1) {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : M},
(x ∈ ⊥) = (x = 0) | false |
Submonoid.mk_inv_mul_mk_eq_one | Mathlib.Algebra.Group.Submonoid.Units | ∀ {M : Type u_1} [inst : Monoid M] (S : Submonoid M) {x : Mˣ} (h : x ∈ S.units),
⟨(Units.coeHom M) x⁻¹, ⋯⟩ * ⟨(Units.coeHom M) x, ⋯⟩ = 1 | true |
Lean.Server.Test.Runner.Client.HighlightedMsgEmbed.goal.elim | Lean.Server.Test.Runner | {motive_1 : Lean.Server.Test.Runner.Client.HighlightedMsgEmbed → Sort u} →
(t : Lean.Server.Test.Runner.Client.HighlightedMsgEmbed) →
t.ctorIdx = 1 →
((a : Lean.Server.Test.Runner.Client.InteractiveGoal) →
motive_1 (Lean.Server.Test.Runner.Client.HighlightedMsgEmbed.goal a)) →
motive_1 t | false |
Lean.Elab.Term.LetRecDeclView.mk.inj | Lean.Elab.LetRec | ∀ {ref : Lean.Syntax} {attrs : Array Lean.Elab.Attribute} {shortDeclName declName : Lean.Name}
{parentName? : Option Lean.Name} {binderIds : Array Lean.Syntax} {binders : Lean.Syntax} {type mvar : Lean.Expr}
{valStx : Lean.Syntax} {termination : Lean.Elab.TerminationHints}
{docString? : Option (Lean.TSyntax `Lean... | true |
_aux_Mathlib_Combinatorics_Quiver_Basic___unexpand_Quiver_Hom_1 | Mathlib.Combinatorics.Quiver.Basic | Lean.PrettyPrinter.Unexpander | false |
_private.Mathlib.Algebra.GCDMonoid.Basic.0.normalizationMonoidOfMonoidHomRightInverse._simp_1 | Mathlib.Algebra.GCDMonoid.Basic | ∀ {α : Type u} [inst : Monoid α] {u v : αˣ}, (u = v) = (↑u = ↑v) | false |
AlgebraicGeometry.Scheme.Modules.pushforwardId | Mathlib.AlgebraicGeometry.Modules.Sheaf | (X : AlgebraicGeometry.Scheme) →
AlgebraicGeometry.Scheme.Modules.pushforward (CategoryTheory.CategoryStruct.id X) ≅
CategoryTheory.Functor.id X.Modules | true |
Ideal.quotientToQuotientRangePowQuotSucc | Mathlib.NumberTheory.RamificationInertia.Basic | {R : Type u} →
[inst : CommRing R] →
{S : Type v} →
[inst_1 : CommRing S] →
[inst_2 : Algebra R S] →
(p : Ideal R) →
(P : Ideal S) →
[hfp : NeZero (p.ramificationIdx P)] →
{i : ℕ} →
{a : S} →
a ∈ P ^ i →
... | true |
CategoryTheory.MonoidalLinear.whiskerLeft_smul | Mathlib.CategoryTheory.Monoidal.Linear | ∀ {R : Type u_1} {inst : Semiring R} {C : Type u_2} {inst_1 : CategoryTheory.Category.{v_1, u_2} C}
{inst_2 : CategoryTheory.Preadditive C} {inst_3 : CategoryTheory.Linear R C}
{inst_4 : CategoryTheory.MonoidalCategory C} {inst_5 : CategoryTheory.MonoidalPreadditive C}
[self : CategoryTheory.MonoidalLinear R C] (... | true |
EReal.sub_le_iff_le_add | Mathlib.Data.EReal.Operations | ∀ {a b c : EReal}, b ≠ ⊥ ∨ c ≠ ⊤ → b ≠ ⊤ ∨ c ≠ ⊥ → (a - b ≤ c ↔ a ≤ c + b) | true |
CategoryTheory.Subobject.ofMkLE | Mathlib.CategoryTheory.Subobject.Basic | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{B A : C} →
(f : A ⟶ B) →
[inst_1 : CategoryTheory.Mono f] →
(X : CategoryTheory.Subobject B) →
CategoryTheory.Subobject.mk f ≤ X → (A ⟶ CategoryTheory.Subobject.underlying.obj X) | true |
ContinuousAffineMap.const_contLinear | Mathlib.Topology.Algebra.ContinuousAffineMap | ∀ {R : Type u_1} {V : Type u_2} {W : Type u_3} {P : Type u_4} {Q : Type u_5} [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 Q] [inst_8 : AddTorsor W Q] [inst_9 : Topolog... | true |
CategoryTheory.ObjectProperty.Is.rec | Mathlib.CategoryTheory.ObjectProperty.Basic | {C : Type u} →
[inst : CategoryTheory.CategoryStruct.{v, u} C] →
{P : CategoryTheory.ObjectProperty C} →
{X : C} → {motive : P.Is X → Sort u_1} → ((prop : P X) → motive ⋯) → (t : P.Is X) → motive t | false |
Std.ExtTreeSet.mem_inter_iff | Std.Data.ExtTreeSet.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t₁ t₂ : Std.ExtTreeSet α cmp} [inst : Std.TransCmp cmp] {k : α},
k ∈ t₁ ∩ t₂ ↔ k ∈ t₁ ∧ k ∈ t₂ | true |
HeytAlg.ext_iff | Mathlib.Order.Category.HeytAlg | ∀ {X Y : HeytAlg} {f g : X ⟶ Y},
f = g ↔ ∀ (x : ↑X), (CategoryTheory.ConcreteCategory.hom f) x = (CategoryTheory.ConcreteCategory.hom g) x | true |
convexHull_neg | Mathlib.Analysis.Convex.Hull | ∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] (s : Set E), (convexHull 𝕜) (-s) = -(convexHull 𝕜) s | true |
CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData_i | Mathlib.Algebra.Homology.ShortComplex.Abelian | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
(S : CategoryTheory.ShortComplex C) {kf : CategoryTheory.Limits.KernelFork S.g}
{cc : CategoryTheory.Limits.CokernelCofork S.f} (hkf : CategoryTheory.Limits.IsLimit kf)
(hcc : CategoryTheory.Limits.IsColimit cc) {H : C} {... | true |
Lean.Elab.MonadParentDecl.casesOn | Lean.Elab.InfoTree.Types | {m : Type → Type} →
{motive : Lean.Elab.MonadParentDecl m → Sort u} →
(t : Lean.Elab.MonadParentDecl m) →
((getParentDeclName? : m (Option Lean.Name)) → motive { getParentDeclName? := getParentDeclName? }) → motive t | false |
_private.Lean.Parser.Basic.0.Lean.Parser.rawStrLitFnAux.errorUnterminated | Lean.Parser.Basic | String.Pos.Raw → Lean.Parser.ParserState → Lean.Parser.ParserState | true |
RingEquiv.piOptionEquivProd | Mathlib.Algebra.Ring.Equiv | {ι : Type u_7} →
{R : Option ι → Type u_8} →
[inst : (i : Option ι) → NonUnitalNonAssocSemiring (R i)] →
((i : Option ι) → R i) ≃+* R none × ((i : ι) → R (some i)) | true |
_private.Mathlib.Analysis.Analytic.Composition.0.HasFPowerSeriesWithinAt.comp._simp_1_1 | Mathlib.Analysis.Analytic.Composition | ∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, (a < min b c) = (a < b ∧ a < c) | false |
instSubsingleton | Init.Core | ∀ (p : Prop), Subsingleton p | true |
Complex.isAlgebraic_sin_rat_mul_pi | Mathlib.NumberTheory.Niven | ∀ (q : ℚ), IsAlgebraic ℤ (Complex.sin (↑q * ↑Real.pi)) | true |
Lean.Parser.Command.recommended_spelling._regBuiltin.Lean.Parser.Command.recommended_spelling.formatter_7 | Lean.Parser.Command | IO Unit | false |
Pi.evalNonUnitalRingHom._proof_2 | Mathlib.Algebra.Ring.Pi | ∀ {I : Type u_2} (f : I → Type u_1) [inst : (i : I) → NonUnitalNonAssocSemiring (f i)] (i : I) (x y : (i : I) → f i),
(↑(Pi.evalAddMonoidHom f i)).toFun (x + y) =
(↑(Pi.evalAddMonoidHom f i)).toFun x + (↑(Pi.evalAddMonoidHom f i)).toFun y | false |
CategoryTheory.Cokleisli.mk._flat_ctor | Mathlib.CategoryTheory.Monad.Kleisli | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {U : CategoryTheory.Comonad C} → C → CategoryTheory.Cokleisli U | false |
ContDiffBump.rOut | Mathlib.Analysis.Calculus.BumpFunction.Basic | {E : Type u_1} → {c : E} → ContDiffBump c → ℝ | true |
NormedAddCommGroup.ofCoreReplaceTopology._proof_1 | Mathlib.Analysis.Normed.Module.Basic | ∀ {𝕜 : Type u_2} {E : Type u_1} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : Norm E]
[T : TopologicalSpace E] (core : NormedSpace.Core 𝕜 E) (H : T = PseudoEMetricSpace.toUniformSpace.toTopologicalSpace)
{x y : E}, dist x y = 0 → x = y | false |
ContinuousLinearEquiv.summable | Mathlib.Topology.Algebra.InfiniteSum.Module | ∀ {ι : Type u_5} {R : Type u_7} {R₂ : Type u_8} {M : Type u_9} {M₂ : Type u_10} [inst : Semiring R]
[inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : AddCommMonoid M₂]
[inst_5 : Module R₂ M₂] [inst_6 : TopologicalSpace M] [inst_7 : TopologicalSpace M₂] {σ : R →+* R₂} {σ' : R₂ →+* R}
... | true |
Std.HashSet.Raw.Equiv.of_forall_contains_eq | Std.Data.HashSet.RawLemmas | ∀ {α : Type u} [inst : BEq α] [inst_1 : Hashable α] {m₁ m₂ : Std.HashSet.Raw α} [LawfulBEq α],
m₁.WF → m₂.WF → (∀ (k : α), m₁.contains k = m₂.contains k) → m₁.Equiv m₂ | true |
Lean.initFn._@.Lean.PrettyPrinter.Delaborator.Options.74134663._hygCtx._hyg.4 | Lean.PrettyPrinter.Delaborator.Options | IO (Lean.Option Bool) | false |
FreeAddMonoid.casesOn_zero | Mathlib.Algebra.FreeMonoid.Basic | ∀ {α : Type u_1} {C : FreeAddMonoid α → Sort u_6} (h0 : C 0)
(ih : (x : α) → (xs : FreeAddMonoid α) → C (FreeAddMonoid.of x + xs)), FreeAddMonoid.casesOn 0 h0 ih = h0 | true |
ContinuousMap.coeFnRingHom_apply | Mathlib.Topology.ContinuousMap.Algebra | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : Semiring β]
[inst_3 : IsTopologicalSemiring β] (f : C(α, β)) (a : α), ContinuousMap.coeFnRingHom f a = f a | true |
_private.Std.Sync.Broadcast.0.Std.Bounded.State.size | Std.Sync.Broadcast | {α : Type} → Std.Bounded.State✝ α → ℕ | true |
Vector.findFinIdx?_subtype | Init.Data.Vector.Find | ∀ {α : Type u_1} {n : ℕ} {p : α → Prop} {xs : Vector { x // p x } n} {f : { x // p x } → Bool} {g : α → Bool},
(∀ (x : α) (h : p x), f ⟨x, h⟩ = g x) → Vector.findFinIdx? f xs = Vector.findFinIdx? g xs.unattach | true |
AffineIsometryEquiv._sizeOf_1 | Mathlib.Analysis.Normed.Affine.Isometry | {𝕜 : Type u_1} →
{V : Type u_2} →
{V₂ : Type u_5} →
{P : Type u_10} →
{P₂ : Type u_11} →
{inst : NormedField 𝕜} →
{inst_1 : SeminormedAddCommGroup V} →
{inst_2 : NormedSpace 𝕜 V} →
{inst_3 : PseudoMetricSpace P} →
{inst_4 : Nor... | false |
Lean.Lsp.DocumentFilter.rec | Lean.Data.Lsp.Basic | {motive : Lean.Lsp.DocumentFilter → Sort u} →
((language? scheme? pattern? : Option String) →
motive { language? := language?, scheme? := scheme?, pattern? := pattern? }) →
(t : Lean.Lsp.DocumentFilter) → motive t | false |
_private.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic.0.vectorSpan_range_eq_span_range_vsub_right_ne._simp_1_1 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | ∀ {α : Type u} {ι : Sort u_1} {f : ι → α} {x : α}, (x ∈ Set.range f) = ∃ y, f y = x | false |
Inner.noConfusionType | Mathlib.Analysis.InnerProductSpace.Defs | Sort u → {𝕜 : Type u_4} → {E : Type u_5} → Inner 𝕜 E → {𝕜' : Type u_4} → {E' : Type u_5} → Inner 𝕜' E' → Sort u | false |
PUnit.mulActionWithZero._proof_1 | Mathlib.Algebra.Module.PUnit | ∀ {R : Type u_2} [inst : MonoidWithZero R] (a : R), a • 0 = 0 | false |
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