name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
addMonoidHomOfMemClosureRangeCoe_apply | Mathlib.Topology.Algebra.Monoid | ∀ {M₁ : Type u_6} {M₂ : Type u_7} [inst : TopologicalSpace M₂] [inst_1 : T2Space M₂] [inst_2 : AddZeroClass M₁]
[inst_3 : AddZeroClass M₂] [inst_4 : ContinuousAdd M₂] {F : Type u_8} [inst_5 : FunLike F M₁ M₂]
[inst_6 : AddMonoidHomClass F M₁ M₂] (f : M₁ → M₂) (hf : f ∈ closure (Set.range fun f x => f x)),
⇑(addMo... | true |
ExpChar.zero | Mathlib.Algebra.CharP.Defs | ∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R], ExpChar R 1 | true |
UInt8.toUInt16_div | Init.Data.UInt.Lemmas | ∀ (a b : UInt8), (a / b).toUInt16 = a.toUInt16 / b.toUInt16 | true |
Rat.instSemilatticeInf | Mathlib.Algebra.Order.Ring.Unbundled.Rat | SemilatticeInf ℚ | true |
CategoryTheory.Subfunctor.range_eq_top | Mathlib.CategoryTheory.Subfunctor.Image | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F F' : CategoryTheory.Functor C (Type w)} (p : F' ⟶ F)
[CategoryTheory.Epi p], CategoryTheory.Subfunctor.range p = ⊤ | true |
Associates.instCommMonoidWithZero._proof_1 | Mathlib.Algebra.GroupWithZero.Associated | ∀ {M : Type u_1} [inst : CommMonoidWithZero M] (a : M), 0 * Associates.mk a = 0 | false |
ISize.minValue_le_toInt | Init.Data.SInt.Lemmas | ∀ (x : ISize), ISize.minValue.toInt ≤ x.toInt | true |
ContinuousLinearMap.isPositive_self_comp_adjoint | Mathlib.Analysis.InnerProductSpace.Positive | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : CompleteSpace E] [inst_6 : CompleteSpace F] (S : E →L[𝕜] F),
(S.comp (ContinuousLinearMap.adjoint S)).Is... | true |
Std.DTreeMap.Internal.Impl.Const.getKey!_insertManyIfNewUnit!_list_of_not_mem_of_mem | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α fun x => Unit} [Std.TransOrd α] [inst : Inhabited α],
t.WF →
∀ {l : List α} {k k' : α},
compare k k' = Ordering.eq →
k ∉ t →
List.Pairwise (fun a b => ¬compare a b = Ordering.eq) l →
k ∈ l → (↑(Std.DTreeMap.Inte... | true |
Aesop.Frontend.AttrConfig.noConfusionType | Aesop.Frontend.Attribute | Sort u → Aesop.Frontend.AttrConfig → Aesop.Frontend.AttrConfig → Sort u | false |
Std.TreeSet.le_max!_of_mem | Std.Data.TreeSet.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet α cmp} [Std.TransCmp cmp] [inst : Inhabited α] {k : α},
k ∈ t → (cmp k t.max!).isLE = true | true |
CategoryTheory.Abelian.SpectralObject.homologyDataIdId_right_p | Mathlib.Algebra.Homology.SpectralObject.Page | ∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} ι] [inst_2 : CategoryTheory.Abelian C]
(X : CategoryTheory.Abelian.SpectralObject C ι) {i j : ι} (f : i ⟶ j) (n₀ n₁ n₂ : ℤ)
(hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObjec... | true |
Std.ExtHashSet.ext_mem | Std.Data.ExtHashSet.Lemmas | ∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} [inst : LawfulBEq α] {m₁ m₂ : Std.ExtHashSet α},
(∀ (k : α), k ∈ m₁ ↔ k ∈ m₂) → m₁ = m₂ | true |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.EMatchTheoremKind.toAttributeCore.match_1 | Lean.Meta.Tactic.Grind.EMatchTheorem | (motive : Lean.Meta.Grind.EMatchTheoremKind → Sort u_1) →
(kind : Lean.Meta.Grind.EMatchTheoremKind) →
(Unit → motive (Lean.Meta.Grind.EMatchTheoremKind.eqLhs true)) →
(Unit → motive (Lean.Meta.Grind.EMatchTheoremKind.eqLhs false)) →
(Unit → motive (Lean.Meta.Grind.EMatchTheoremKind.eqRhs true)) →
... | false |
Sigma.forall | Mathlib.Data.Sigma.Basic | ∀ {α : Type u_1} {β : α → Type u_4} {p : (a : α) × β a → Prop},
(∀ (x : (a : α) × β a), p x) ↔ ∀ (a : α) (b : β a), p ⟨a, b⟩ | true |
Lean._aux_Init_Meta___macroRules_Lean_Parser_Syntax_addPrio_1 | Init.Meta | Lean.Macro | false |
SchwartzMap.instIsUniformAddGroup | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | ∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F], IsUniformAddGroup (SchwartzMap E F) | true |
ChainComplex.truncateAugment._proof_3 | Mathlib.Algebra.Homology.Augment | ∀ {V : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} V] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V]
(C : ChainComplex V ℕ) {X : V} (f : C.X 0 ⟶ X) (w : CategoryTheory.CategoryStruct.comp (C.d 1 0) f = 0) (i j : ℕ),
(ComplexShape.down ℕ).Rel i j →
CategoryTheory.CategoryStruct.comp (CategoryTheory... | false |
Lean.Elab.Tactic.Do.ProofMode.ensureMGoal | Lean.Elab.Tactic.Do.ProofMode.MGoal | Lean.Elab.Tactic.TacticM (Lean.MVarId × Lean.Elab.Tactic.Do.ProofMode.MGoal) | true |
NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply | Mathlib.NumberTheory.NumberField.CMField | ∀ (F : Type u_1) (K : Type u_2) [inst : Field F] [inst_1 : NumberField.IsTotallyReal F] [inst_2 : Field K]
[inst_3 : CharZero K] [inst_4 : Algebra.IsIntegral ℚ K] [inst_5 : NumberField.IsTotallyComplex K]
[inst_6 : Algebra F K] [inst_7 : Algebra.IsQuadraticExtension F K] (x : ↥(NumberField.maximalRealSubfield K)),
... | true |
IsLocalization.Away.awayToAwayRight_eq | Mathlib.RingTheory.Localization.Away.Basic | ∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {P : Type u_3}
[inst_3 : CommSemiring P] (x : R) [inst_4 : IsLocalization.Away x S] (y : R) [inst_5 : Algebra R P]
[inst_6 : IsLocalization.Away (x * y) P] (a : R),
(IsLocalization.Away.awayToAwayRight x y) ((... | true |
Int.mul_le_mul_left._simp_1 | Init.Data.Int.DivMod.Lemmas | ∀ {a b c : ℤ}, 0 < a → (a * b ≤ a * c) = (b ≤ c) | false |
EReal.Tendsto.const_mul | Mathlib.Topology.Instances.EReal.Lemmas | ∀ {α : Type u_2} {f : Filter α} {m : α → EReal} {a b : EReal},
Filter.Tendsto m f (nhds b) → a ≠ ⊥ ∨ b ≠ 0 → a ≠ ⊤ ∨ b ≠ 0 → Filter.Tendsto (fun b => a * m b) f (nhds (a * b)) | true |
Lean.Elab.Command.AssertExists._sizeOf_1 | Lean.Elab.AssertExists | Lean.Elab.Command.AssertExists → ℕ | false |
CategoryTheory.Discrete.monoidalFunctorMonoidal._proof_10 | Mathlib.CategoryTheory.Monoidal.Discrete | ∀ {M : Type u_1} [inst : Monoid M] {N : Type u_2} [inst_1 : Monoid N] (F : M →* N) (X : CategoryTheory.Discrete M),
(CategoryTheory.MonoidalCategoryStruct.rightUnitor ((CategoryTheory.Discrete.monoidalFunctor F).obj X)).hom =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerL... | false |
_private.Mathlib.Topology.Bornology.BoundedOperation.0.isBounded_pow._simp_1_2 | Mathlib.Topology.Bornology.BoundedOperation | ∀ {α : Type u} {β : Type v} (f : α → β) (s : Set α) (y : β), (y ∈ f '' s) = ∃ x ∈ s, f x = y | false |
Multiset.le_union_left | Mathlib.Data.Multiset.UnionInter | ∀ {α : Type u_1} [inst : DecidableEq α] {s t : Multiset α}, s ≤ s ∪ t | true |
SzemerediRegularity.coe_stepBound | Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | ∀ {α : Type u_1} [inst : Semiring α] (n : ℕ), ↑(SzemerediRegularity.stepBound n) = ↑n * 4 ^ n | true |
HomologicalComplex.Hom.ext_iff | 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} {A B : HomologicalComplex V c}
{x y : A.Hom B}, x = y ↔ x.f = y.f | true |
BooleanSubalgebra.sSup_mem | Mathlib.Order.BooleanSubalgebra | ∀ {α : Type u_2} [inst : CompleteBooleanAlgebra α] {L : BooleanSubalgebra α} {s : Set α}, s.Finite → s ⊆ ↑L → sSup s ∈ L | true |
Concept.strictAnti_intent | Mathlib.Order.Concept | ∀ {α : Type u_2} {β : Type u_3} {r : α → β → Prop}, StrictAnti Concept.intent | true |
AddSubgroup.inf_addSubgroupOf_left | Mathlib.Algebra.Group.Subgroup.Map | ∀ {G : Type u_1} [inst : AddGroup G] (H K : AddSubgroup G), (K ⊓ H).addSubgroupOf K = H.addSubgroupOf K | true |
_private.Init.Data.Int.LemmasAux.0.Int.toNat_sub_of_le._proof_1_1 | Init.Data.Int.LemmasAux | ∀ {a b : ℤ}, b ≤ a → ¬↑(a - b).toNat = a - b → False | false |
ULift.nonUnitalNonAssocSemiring._proof_3 | Mathlib.Algebra.Ring.ULift | ∀ {R : Type u_2} [inst : NonUnitalNonAssocSemiring R] (a : ULift.{u_1, u_2} R), 0 * a = 0 | false |
Polynomial.content.eq_1 | Mathlib.RingTheory.Polynomial.Content | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] (p : Polynomial R),
p.content = p.support.gcd p.coeff | true |
CochainComplex.singleFunctors._proof_8 | Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors | ∀ (C : Type u_1) [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] (n m a a' a'' : ℤ) (ha' : n + a = a') (ha'' : m + a' = a''),
CategoryTheory.NatIso.ofComponents
(fun X => HomologicalComplex.Hom.isoOfComponents (fun i => Cat... | false |
CategoryTheory.Functor.sheafInducedTopologyEquivOfIsCoverDense._proof_1 | Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} C] {D : Type u_4}
[inst_1 : CategoryTheory.Category.{u_2, u_4} D] (G : CategoryTheory.Functor C D)
(K : CategoryTheory.GrothendieckTopology D) [inst_2 : G.LocallyCoverDense K] [inst_3 : G.IsLocallyFull K]
[inst_4 : G.IsLocallyFaithful K] [G.IsCoverDense ... | false |
Semiquot.IsPure | Mathlib.Data.Semiquot | {α : Type u_1} → Semiquot α → Prop | true |
CategoryTheory.Limits.CatCospanTransform.category | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | {A : Type u₁} →
{B : Type u₂} →
{C : Type u₃} →
{A' : Type u₄} →
{B' : Type u₅} →
{C' : Type u₆} →
[inst : CategoryTheory.Category.{v₁, u₁} A] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
[inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
... | true |
Vector.map_zip_eq_zipWith | Init.Data.Vector.Zip | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {n : ℕ} {f : α × β → γ} {as : Vector α n} {bs : Vector β n},
Vector.map f (as.zip bs) = Vector.zipWith (Function.curry f) as bs | true |
Lean.Grind.AC.Seq.startsWithVar_k_cons | Init.Grind.AC | ∀ (y x : Lean.Grind.AC.Var) (s : Lean.Grind.AC.Seq), (Lean.Grind.AC.Seq.cons y s).startsWithVar_k x = (x == y) | true |
LieAlgebra.LoopAlgebra.residuePairing._proof_3 | Mathlib.Algebra.Lie.Loop | ∀ (R : Type u_1) (A : Type u_2) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : AddCommGroup A] [inst_4 : DistribSMul A R] (Φ : LinearMap.BilinForm R L)
(f x y : LieAlgebra.loopAlgebra R A L),
(((LieAlgebra.LoopAlgebra.toFinsupp R A L) (x + y)).sum fun a v =>
a • ... | false |
Lean.Omega.Int.add_le_zero_iff_le_neg | Init.Omega.Int | ∀ {a b : ℤ}, a + b ≤ 0 ↔ a ≤ -b | true |
_private.Mathlib.Analysis.Complex.Periodic.0.Function.Periodic.qParam_ne_zero._simp_1_2 | Mathlib.Analysis.Complex.Periodic | ∀ (x : ℂ), (Complex.exp x = 0) = False | false |
ENat.epow_zero | Mathlib.Data.ENat.Pow | ∀ {x : ℕ∞}, x ^ 0 = 1 | true |
Filter.indicator_const_eventuallyEq | Mathlib.Order.Filter.IndicatorFunction | ∀ {α : Type u_1} {β : Type u_2} [inst : Zero β] {l : Filter α} {c : β},
c ≠ 0 → ∀ {s t : Set α}, ((s.indicator fun x => c) =ᶠ[l] t.indicator fun x => c) ↔ s =ᶠ[l] t | true |
Cardinal.mul_natCast_lt_mul_natCast._simp_1 | Mathlib.SetTheory.Cardinal.Arithmetic | ∀ {n : ℕ} {a b : Cardinal.{u_1}}, n ≠ 0 → (a * ↑n < b * ↑n) = (a < b) | false |
ContinuousMapZero.instCanLift | Mathlib.Topology.ContinuousMap.ContinuousMapZero | ∀ {X : Type u_1} {R : Type u_2} [inst : Zero X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace R]
[inst_3 : CommSemiring R], CanLift C(X, R) (ContinuousMapZero X R) toContinuousMap fun f => f 0 = 0 | true |
List.drop.eq_2 | Init.Data.Array.GetLit | ∀ {α : Type u} (n : ℕ), List.drop n.succ [] = [] | true |
Int32.or_comm | Init.Data.SInt.Bitwise | ∀ (a b : Int32), a ||| b = b ||| a | true |
Flow.isSemiconjugacy_id_iff_eq | Mathlib.Dynamics.Flow | ∀ {τ : Type u_1} [inst : AddMonoid τ] [inst_1 : TopologicalSpace τ] [inst_2 : ContinuousAdd τ] {α : Type u_2}
[inst_3 : TopologicalSpace α] (ϕ ψ : Flow τ α), Flow.IsSemiconjugacy id ϕ ψ ↔ ϕ = ψ | true |
AlgebraicGeometry.Scheme.isLocallyArtinianScheme_Spec | Mathlib.AlgebraicGeometry.Artinian | ∀ {R : CommRingCat}, AlgebraicGeometry.IsLocallyArtinian (AlgebraicGeometry.Spec R) ↔ IsArtinianRing ↑R | true |
Projectivization.lift_mk | Mathlib.LinearAlgebra.Projectivization.Basic | ∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {α : Type u_3}
(f : { v // v ≠ 0 } → α) (hf : ∀ (a b : { v // v ≠ 0 }) (t : K), ↑a = t • ↑b → f a = f b) (v : V) (hv : v ≠ 0),
Projectivization.lift f hf (Projectivization.mk K v hv) = f ⟨v, hv⟩ | true |
Nonneg.linearOrderedCommGroupWithZero._proof_5 | Mathlib.Algebra.Order.Nonneg.Field | ∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α], Nontrivial { x // 0 ≤ x } | false |
AlgCat.instMonoidalCategory | Mathlib.Algebra.Category.AlgCat.Monoidal | {R : Type u} → [inst : CommRing R] → CategoryTheory.MonoidalCategory (AlgCat R) | true |
Std.Rxo.Iterator.mk.noConfusion | Init.Data.Range.Polymorphic.RangeIterator | {α : Type u} →
{P : Sort u_1} →
{next : Option α} →
{upperBound : α} →
{next' : Option α} →
{upperBound' : α} →
{ next := next, upperBound := upperBound } = { next := next', upperBound := upperBound' } →
(next ≍ next' → upperBound ≍ upperBound' → P) → P | false |
SimpleGraph.Walk.nil_nil._simp_1 | Mathlib.Combinatorics.SimpleGraph.Walks.Basic | ∀ {V : Type u} {G : SimpleGraph V} {u : V}, SimpleGraph.Walk.nil.Nil = True | false |
CategoryTheory.Adjunction.corepresentableBy._proof_1 | Mathlib.CategoryTheory.Adjunction.Basic | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
[inst_1 : CategoryTheory.Category.{u_1, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
(adj : F ⊣ G) (X : C) {Y Y' : D} (g : Y ⟶ Y') (f : F.obj X ⟶ Y),
(adj.homEquiv X Y') (CategoryTheory.CategoryStruct.comp f... | false |
RingHom.instMonoid._proof_1 | Mathlib.Algebra.Ring.Hom.Defs | ∀ {α : Type u_1} {x : NonAssocSemiring α} (n : ℕ) (f : α →+* α), (⇑f)^[n] = ⇑(npowRec n f) | false |
Nat.shiftLeft'.eq_1 | Mathlib.Data.Nat.Bits | ∀ (b : Bool) (m : ℕ), Nat.shiftLeft' b m 0 = m | true |
QuadraticForm.isometryEquivWeightedSumSquares._proof_3 | Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv | ∀ {K : Type u_1} [inst : Field K], SMulCommClass K K K | false |
CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctor | Mathlib.CategoryTheory.Sites.Point.Skyscraper | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{J : CategoryTheory.GrothendieckTopology C} →
J.Point →
{A : Type u'} →
[inst_1 : CategoryTheory.Category.{v', u'} A] →
[CategoryTheory.Limits.HasProducts A] → CategoryTheory.Functor A (CategoryTheory.Sheaf J A) | true |
Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput.recOn | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Carry | {α : Type} →
[inst : Hashable α] →
[inst_1 : DecidableEq α] →
{aig : Std.Sat.AIG α} →
{motive : Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput aig → Sort u} →
(t : Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput aig) →
((w : ℕ) → (vec : aig.BinaryRefVec w) → (cin : aig.Ref... | false |
CategoryTheory.ObjectProperty.IsSeparating.isDetecting | Mathlib.CategoryTheory.Generator.Basic | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.ObjectProperty C}
[CategoryTheory.Balanced C], P.IsSeparating → P.IsDetecting | true |
initFn._@.Mathlib.Tactic.TacticAnalysis.Declarations.66427035._hygCtx._hyg.4 | Mathlib.Tactic.TacticAnalysis.Declarations | IO (Lean.Option Bool) | false |
_private.Mathlib.LinearAlgebra.SesquilinearForm.Basic.0.LinearMap.isOrtho_flip._simp_1_1 | Mathlib.LinearAlgebra.SesquilinearForm.Basic | ∀ {R : Type u_1} {R₁ : Type u_2} {R₂ : Type u_3} {M : Type u_5} {M₁ : Type u_6} {M₂ : Type u_7} [inst : CommSemiring R]
[inst_1 : CommSemiring R₁] [inst_2 : AddCommMonoid M₁] [inst_3 : Module R₁ M₁] [inst_4 : CommSemiring R₂]
[inst_5 : AddCommMonoid M₂] [inst_6 : Module R₂ M₂] [inst_7 : AddCommMonoid M] [inst_8 : M... | false |
_private.Lean.Parser.Extension.0.Lean.Parser.addParserCategoryCore | Lean.Parser.Extension | Lean.Parser.ParserCategories → Lean.Name → Lean.Parser.ParserCategory → Except String Lean.Parser.ParserCategories | true |
Submodule.topEquiv | Mathlib.Algebra.Module.Submodule.Lattice | {R : Type u_1} → {M : Type u_3} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → ↥⊤ ≃ₗ[R] M | true |
AddAction.block_stabilizerOrderIso.match_5 | Mathlib.GroupTheory.GroupAction.Blocks | ∀ (G : Type u_2) [inst : AddGroup G] {X : Type u_1} [inst_1 : AddAction G X] (a : X)
(motive : { B // a ∈ B ∧ AddAction.IsBlock G B } → Prop) (x : { B // a ∈ B ∧ AddAction.IsBlock G B }),
(∀ (val : Set X) (ha : a ∈ val) (hB : AddAction.IsBlock G val), motive ⟨val, ⋯⟩) → motive x | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walks.Operations.0.SimpleGraph.Walk.drop.match_1.eq_3 | Mathlib.Combinatorics.SimpleGraph.Walks.Operations | ∀ {V : Type u_1} {G : SimpleGraph V} {u : V} (motive : (v : V) → G.Walk u v → ℕ → Sort u_2) (v v_1 : V)
(h : G.Adj u v_1) (q : G.Walk v_1 v) (n : ℕ) (h_1 : (x : ℕ) → motive u SimpleGraph.Walk.nil x)
(h_2 : (v : V) → (p : G.Walk u v) → motive v p 0)
(h_3 : (v v_2 : V) → (h : G.Adj u v_2) → (q : G.Walk v_2 v) → (n ... | true |
_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.Action.isSorryAlt._sparseCasesOn_1 | Lean.Meta.Tactic.Grind.Split | {α : Type u} →
{motive : List α → Sort u_1} →
(t : List α) →
((head : α) → (tail : List α) → motive (head :: tail)) → (Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t | false |
Std.DTreeMap.Internal.Impl.minKey?.eq_def | Std.Data.DTreeMap.Internal.Queries | ∀ {α : Type u} {β : α → Type v} (x : Std.DTreeMap.Internal.Impl α β),
x.minKey? =
match x with
| Std.DTreeMap.Internal.Impl.leaf => none
| Std.DTreeMap.Internal.Impl.inner size k v Std.DTreeMap.Internal.Impl.leaf r => some k
| Std.DTreeMap.Internal.Impl.inner size k v (l@h:(Std.DTreeMap.Internal.Impl.... | true |
_private.Mathlib.MeasureTheory.Group.Action.0.MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero.match_1_1 | Mathlib.MeasureTheory.Group.Action | ∀ (G : Type u_1) {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {K U : Set α}
(motive : (∃ I, K ⊆ ⋃ g ∈ I, g +ᵥ U) → Prop) (x : ∃ I, K ⊆ ⋃ g ∈ I, g +ᵥ U),
(∀ (t : Finset G) (ht : K ⊆ ⋃ g ∈ t, g +ᵥ U), motive ⋯) → motive x | false |
CategoryTheory.Limits.CofanTypes | Mathlib.CategoryTheory.Limits.Types.Coproducts | {C : Type u} → (C → Type v) → Type (max (max u v) (w + 1)) | true |
InfHom.top_apply | Mathlib.Order.Hom.Lattice | ∀ {α : Type u_2} {β : Type u_3} [inst : Min α] [inst_1 : SemilatticeInf β] [inst_2 : Top β] (a : α), ⊤ a = ⊤ | true |
CategoryTheory.CostructuredArrow.costructuredArrowToOverEquivalence.functor._proof_3 | Mathlib.CategoryTheory.Comma.Over.Basic | ∀ {T : Type u_4} [inst : CategoryTheory.Category.{u_2, u_4} T] {D : Type u_3}
[inst_1 : CategoryTheory.Category.{u_1, u_3} D] (F : CategoryTheory.Functor D T) {X : T} (Y : CategoryTheory.Over X)
{X_1 Y_1 Z : CategoryTheory.CostructuredArrow (CategoryTheory.CostructuredArrow.toOver F X) Y} (f : X_1 ⟶ Y_1)
(g : Y_1... | false |
Asymptotics.«term_~[_]_» | Mathlib.Analysis.Asymptotics.Defs | Lean.TrailingParserDescr | true |
Ordinal.small_Icc | Mathlib.SetTheory.Ordinal.Basic | ∀ (a b : Ordinal.{u}), Small.{u, u + 1} ↑(Set.Icc a b) | true |
Rack.toEnvelGroup.map._proof_2 | Mathlib.Algebra.Quandle | ∀ {R : Type u_1} [inst : Rack R] {G : Type u_2} [inst_1 : Group G] (f : ShelfHom R (Quandle.Conj G))
(x y : Rack.EnvelGroup R),
Quotient.liftOn (x * y) (Rack.toEnvelGroup.mapAux f) ⋯ =
Quotient.liftOn x (Rack.toEnvelGroup.mapAux f) ⋯ * Quotient.liftOn y (Rack.toEnvelGroup.mapAux f) ⋯ | false |
_private.Mathlib.Topology.UrysohnsLemma.0.Urysohns.CU.approx_le_one._simp_1_4 | Mathlib.Topology.UrysohnsLemma | ∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α), b⁻¹ * a = a / b | false |
continuousAt_iff_lower_upperSemicontinuousAt | Mathlib.Topology.Semicontinuity.Basic | ∀ {α : Type u_1} [inst : TopologicalSpace α] {x : α} {γ : Type u_4} [inst_1 : LinearOrder γ]
[inst_2 : TopologicalSpace γ] [OrderTopology γ] {f : α → γ},
ContinuousAt f x ↔ LowerSemicontinuousAt f x ∧ UpperSemicontinuousAt f x | true |
BoxIntegral.Box.ne_of_disjoint_coe | Mathlib.Analysis.BoxIntegral.Box.Basic | ∀ {ι : Type u_1} {I J : BoxIntegral.Box ι}, Disjoint ↑I ↑J → I ≠ J | true |
Std.ToFormat.format | Init.Data.Format.Basic | {α : Type u} → [self : Std.ToFormat α] → α → Std.Format | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_738 | Mathlib.GroupTheory.Perm.Cycle.Type | ∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w w_1 : α),
List.idxOfNth w [g (g a)] (List.idxOfNth w [g (g a)] 1) + 1 ≤
(List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)]).length →
List.idxOfNth w [g (g a)] (List.idxOfNth w [g (g a)] 1) <
(List.findIdxs (fun x => decide ... | false |
TensorAlgebra.instRing._proof_14 | Mathlib.LinearAlgebra.TensorAlgebra.Basic | ∀ (M : Type u_1) [inst : AddCommMonoid M] {S : Type u_2} [inst_1 : CommRing S] [inst_2 : Module S M],
autoParam (∀ (n : ℕ), IntCast.intCast ↑n = ↑n) AddGroupWithOne.intCast_ofNat._autoParam | false |
_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.eq_indicator_iff._proof_1_3 | Mathlib.Data.Finsupp.Indicator | ∀ {ι : Type u_1} {α : Type u_2} [inst : Zero α] (s : Finset ι) (f : (i : ι) → i ∈ s → α) {g : ι → α},
(∀ (i : ι), if hi : i ∈ s then f i hi = g i else g i = 0) ↔ (∀ (i : ι) (hi : i ∈ s), f i hi = g i) ∧ ∀ i ∉ s, g i = 0 | false |
«term⅟_» | Mathlib.Algebra.Group.Invertible.Defs | Lean.ParserDescr | true |
Sym.cast._proof_4 | Mathlib.Data.Sym.Basic | ∀ {α : Type u_1} {n m : ℕ}, n = m → ∀ (s : Sym α m), (↑s).card = n | false |
Lean.Elab.InfoTree | Lean.Elab.InfoTree.Types | Type | true |
LinearEquiv.piCongrRight_trans | Mathlib.LinearAlgebra.Pi | ∀ {R : Type u} {ι : Type x} [inst : Semiring R] {φ : ι → Type u_1} {ψ : ι → Type u_2} {χ : ι → Type u_3}
[inst_1 : (i : ι) → AddCommMonoid (φ i)] [inst_2 : (i : ι) → Module R (φ i)] [inst_3 : (i : ι) → AddCommMonoid (ψ i)]
[inst_4 : (i : ι) → Module R (ψ i)] [inst_5 : (i : ι) → AddCommMonoid (χ i)] [inst_6 : (i : ι... | true |
CategoryTheory.MonoidalCategory.instMonoidalFunctorTensoringRight._proof_2 | Mathlib.CategoryTheory.Monoidal.End | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y : C}
(f : X ⟶ Y) (X' : C),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerRight ((CategoryTheory.MonoidalCategory.tensoringRight C).map f)
((CategoryTheory... | false |
AlgebraicClosure.instCommRing._proof_46 | Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure | ∀ (k : Type u_1) [inst : Field k],
autoParam (∀ (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)) AddGroupWithOne.intCast_negSucc._autoParam | false |
CategoryTheory.ObjectProperty.instSmallUnopOfOpposite | Mathlib.CategoryTheory.ObjectProperty.Small | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty Cᵒᵖ)
[CategoryTheory.ObjectProperty.Small.{w, v, u} P], CategoryTheory.ObjectProperty.Small.{w, v, u} P.unop | true |
_private.Mathlib.Probability.Moments.Variance.0.ProbabilityTheory.evariance_def'._simp_1_7 | Mathlib.Probability.Moments.Variance | ∀ {a b : Prop}, (a ∨ b) = (¬a → b) | false |
Set.graphOn_univ_inj | Mathlib.Data.Set.Function | ∀ {α : Type u_1} {β : Type u_2} {f g : α → β}, Set.graphOn f Set.univ = Set.graphOn g Set.univ ↔ f = g | true |
ExpGrowth.expGrowthInf_of_eventually_ge | Mathlib.Analysis.Asymptotics.ExpGrowth | ∀ {u v : ℕ → ENNReal} {b : ENNReal},
b ≠ 0 → (∀ᶠ (n : ℕ) in Filter.atTop, b * u n ≤ v n) → ExpGrowth.expGrowthInf u ≤ ExpGrowth.expGrowthInf v | true |
_private.Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable.0.mdifferentiableWithinAt_totalSpace._simp_1_1 | Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | ∀ {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] {E' : Type u_5} [inst_6 : NormedAddComm... | false |
AddAction.zmultiplesQuotientStabilizerEquiv._proof_6 | Mathlib.Data.ZMod.QuotientGroup | ∀ {α : Type u_1} {β : Type u_2} [inst : AddGroup α] (a : α) [inst_1 : AddAction α β] (b : β),
Function.Injective
⇑(QuotientAddGroup.map (AddSubgroup.zmultiples ↑(Function.minimalPeriod (fun x => a +ᵥ x) b))
(AddAction.stabilizer (↥(AddSubgroup.zmultiples a)) b) ((zmultiplesHom ↥(AddSubgroup.zmultiples... | false |
SimpleGraph.Walk.length_dropLast | Mathlib.Combinatorics.SimpleGraph.Walks.Operations | ∀ {V : Type u} {G : SimpleGraph V} {u v : V} (p : G.Walk u v), p.dropLast.length = p.length - 1 | true |
LLVM.addGlobal | Lean.Compiler.IR.LLVMBindings | {ctx : LLVM.Context} → LLVM.Module ctx → String → LLVM.LLVMType ctx → BaseIO (LLVM.Value ctx) | true |
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