name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
List.countP_lt_length_iff._simp_1 | Mathlib.Data.List.Count | ∀ {α : Type u_1} {l : List α} {p : α → Bool}, (List.countP p l < l.length) = ∃ a ∈ l, p a = false | false |
ZeroAtInftyContinuousMap.instAddZeroClass._proof_2 | Mathlib.Topology.ContinuousMap.ZeroAtInfty | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : AddZeroClass β],
⇑0 = 0 | false |
CompleteLatticeHomClass.toFrameHomClass | Mathlib.Order.Hom.CompleteLattice | ∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : FunLike F α β] [inst_1 : CompleteLattice α]
[inst_2 : CompleteLattice β] [CompleteLatticeHomClass F α β], FrameHomClass F α β | true |
zpow_right_strictAnti | Mathlib.Algebra.Order.Group.Basic | ∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] {a : α},
a < 1 → StrictAnti fun n => a ^ n | true |
ProperlyDiscontinuousVAdd.rec | Mathlib.Topology.Algebra.ConstMulAction | {Γ : Type u_4} →
{T : Type u_5} →
[inst : TopologicalSpace T] →
[inst_1 : VAdd Γ T] →
{motive : ProperlyDiscontinuousVAdd Γ T → Sort u} →
((finite_disjoint_inter_image :
∀ {K L : Set T}, IsCompact K → IsCompact L → {γ | ((fun x => γ +ᵥ x) '' K ∩ L).Nonempty}.Finite) →
... | false |
instDecidableEqQuadraticAlgebra.decEq.match_1 | Mathlib.Algebra.QuadraticAlgebra.Defs | {R : Type u_1} →
{a b : R} →
(motive : QuadraticAlgebra R a b → QuadraticAlgebra R a b → Sort u_2) →
(x x_1 : QuadraticAlgebra R a b) →
((a_1 a_2 b_1 b_2 : R) → motive { re := a_1, im := a_2 } { re := b_1, im := b_2 }) → motive x x_1 | false |
CategoryTheory.Functor.relativelyRepresentable.w | Mathlib.CategoryTheory.MorphismProperty.Representable | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F : CategoryTheory.Functor C D} {X Y : D} {f : X ⟶ Y} (hf : F.relativelyRepresentable f) {a : C} (g : F.obj a ⟶ Y),
CategoryTheory.CategoryStruct.comp (hf.fst g) f = CategoryTheory.CategoryStruct... | true |
Set.zero_smul_set_subset | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set | ∀ {α : Type u_1} {β : Type u_2} [inst : Zero α] [inst_1 : Zero β] [inst_2 : SMulWithZero α β] (s : Set β), 0 • s ⊆ 0 | true |
Algebra.FormallyUnramified.of_surjective | Mathlib.RingTheory.Unramified.Basic | ∀ {R : Type u_1} [inst : CommRing R] {A : Type u_2} {B : Type u_3} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[inst_3 : CommRing B] [inst_4 : Algebra R B] [Algebra.FormallyUnramified R A] (f : A →ₐ[R] B),
Function.Surjective ⇑f → Algebra.FormallyUnramified R B | true |
Int.bmod_eq_self_sub_bdiv_mul | Init.Data.Int.DivMod.Lemmas | ∀ (x : ℤ) (m : ℕ), x.bmod m = x - x.bdiv m * ↑m | true |
LieAdmissibleAlgebra.toModule | Mathlib.Algebra.NonAssoc.LieAdmissible.Defs | {R : Type u_1} →
{L : Type u_2} → {inst : CommRing R} → {inst_1 : LieAdmissibleRing L} → [self : LieAdmissibleAlgebra R L] → Module R L | true |
CategoryTheory.Abelian.SpectralObject.kernelSequenceE._proof_2 | Mathlib.Algebra.Homology.SpectralObject.Page | ∀ {C : Type u_2} {ι : Type u_4} [inst : CategoryTheory.Category.{u_1, u_2} C]
[inst_1 : CategoryTheory.Category.{u_3, u_4} ι] [inst_2 : CategoryTheory.Abelian C]
(X : CategoryTheory.Abelian.SpectralObject C ι) {i j k l : ι} (f₁ : i ⟶ j) (f₃ : k ⟶ l) (n₁ n₂ : ℤ),
CategoryTheory.Limits.HasBinaryBiproduct ((X.H n₁).... | false |
_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.eq_1 | Mathlib.Computability.TuringMachine.PostTuringMachine | ∀ {Γ : Type u_1} {Λ : Type u_2} (motive : Turing.TM0to1.Λ' Γ Λ → Sort u_3) (q : Λ)
(h_1 : (q : Λ) → motive (Turing.TM0to1.Λ'.normal q))
(h_2 : (d : Turing.Dir) → (q : Λ) → motive (Turing.TM0to1.Λ'.act (Turing.TM0.Stmt.move d) q))
(h_3 : (a : Γ) → (q : Λ) → motive (Turing.TM0to1.Λ'.act (Turing.TM0.Stmt.write a) q)... | true |
Bundle.Trivialization.piecewise._proof_1 | Mathlib.Topology.FiberBundle.Trivialization | ∀ {B : Type u_2} {F : Type u_3} {Z : Type u_1} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F] {proj : Z → B}
[inst_2 : TopologicalSpace Z] (e e' : Bundle.Trivialization F proj) (s : Set B),
e.baseSet ∩ frontier s = e'.baseSet ∩ frontier s →
e.source ∩ frontier (proj ⁻¹' s) = e'.source ∩ frontier (pro... | false |
Std.TreeSet.Raw.max?_le_max?_insert | Std.Data.TreeSet.Raw.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet.Raw α cmp} [inst : Std.TransCmp cmp] (h : t.WF) {k km kmi : α},
t.max? = some km → (t.insert k).max?.get ⋯ = kmi → (cmp km kmi).isLE = true | true |
ContinuousOn.cpow | Mathlib.Analysis.SpecialFunctions.Pow.Continuity | ∀ {α : Type u_1} [inst : TopologicalSpace α] {f g : α → ℂ} {s : Set α},
ContinuousOn f s → ContinuousOn g s → (∀ a ∈ s, f a ∈ Complex.slitPlane) → ContinuousOn (fun x => f x ^ g x) s | true |
AddCircle.equivIco | Mathlib.Topology.Instances.AddCircle.Defs | {𝕜 : Type u_1} →
[inst : AddCommGroup 𝕜] →
(p : 𝕜) →
[inst_1 : LinearOrder 𝕜] →
[IsOrderedAddMonoid 𝕜] → [hp : Fact (0 < p)] → (a : 𝕜) → [Archimedean 𝕜] → AddCircle p ≃ ↑(Set.Ico a (a + p)) | true |
_private.Std.Time.Date.ValidDate.0.PSigma.casesOn._arg_pusher | Std.Time.Date.ValidDate | ∀ {α : Sort u} {β : α → Sort v} {motive : PSigma β → Sort u_1} (α_1 : Sort u✝) (β_1 : α_1 → Sort v✝)
(f : (x : α_1) → β_1 x) (rel : PSigma β → α_1 → Prop) (t : PSigma β)
(mk : (fst : α) → (snd : β fst) → ((y : α_1) → rel ⟨fst, snd⟩ y → β_1 y) → motive ⟨fst, snd⟩),
(PSigma.casesOn (motive := fun t => ((y : α_1) → ... | false |
MvPolynomial.expand_char | Mathlib.RingTheory.MvPolynomial.Expand | ∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] (p : ℕ) [inst_1 : ExpChar R p] {f : MvPolynomial σ R},
(MvPolynomial.map (frobenius R p)) ((MvPolynomial.expand p) f) = f ^ p | true |
Mathlib.Util.«_aux_Mathlib_Util_CompileInductive___elabRules_Mathlib_Util_commandCompile_def%__1» | Mathlib.Util.CompileInductive | Lean.Elab.Command.CommandElab | false |
Int32.toInt_not | Init.Data.SInt.Bitwise | ∀ (a : Int32), (~~~a).toInt = (-a.toInt - 1).bmod (2 ^ 32) | true |
PointedCone.lineal._proof_4 | Mathlib.Geometry.Convex.Cone.Pointed | ∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsOrderedRing R], PosMulMono R | false |
SubMulAction.subtype_eq_val | Mathlib.GroupTheory.GroupAction.SubMulAction | ∀ {R : Type u} {M : Type v} [inst : SMul R M] (p : SubMulAction R M), ⇑p.subtype = Subtype.val | true |
Lean.Elab.Term.State.mk.injEq | Lean.Elab.Term.TermElabM | ∀ (levelNames : List Lean.Name) (syntheticMVars : Lean.MVarIdMap Lean.Elab.Term.SyntheticMVarDecl)
(pendingMVars : List Lean.MVarId) (mvarErrorInfos : List Lean.Elab.Term.MVarErrorInfo)
(levelMVarErrorInfos : List Lean.Elab.Term.LevelMVarErrorInfo) (mvarArgNames : Lean.MVarIdMap Lean.Name)
(letRecsToLift : List L... | true |
Encodable.decode₂_is_partial_inv | Mathlib.Logic.Encodable.Basic | ∀ {α : Type u_1} [inst : Encodable α], Function.IsPartialInv Encodable.encode (Encodable.decode₂ α) | true |
Polynomial.Monic.degree_le_zero_iff_eq_one | Mathlib.Algebra.Polynomial.Monic | ∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.Monic → (p.degree ≤ 0 ↔ p = 1) | true |
Ordinal.nfp_mul_eq_opow_omega0 | Mathlib.SetTheory.Ordinal.FixedPoint | ∀ {a b : Ordinal.{u_1}}, 0 < b → b ≤ a ^ Ordinal.omega0 → Ordinal.nfp (fun x => a * x) b = a ^ Ordinal.omega0 | true |
instFullWitness | Mathlib.CategoryTheory.UnivLE | ∀ [inst : UnivLE.{max u v, v}], UnivLE.witness.Full | true |
_private.Mathlib.Topology.ContinuousMap.CompactlySupported.0.CompactlySupportedContinuousMap.nnrealPart_smul_neg._simp_1_2 | Mathlib.Topology.ContinuousMap.CompactlySupported | ∀ {R : Type u} [inst : Semiring R] [inst_1 : Preorder R] {a b : R} [ExistsAddOfLE R] [MulPosMono R] [AddRightMono R]
[AddRightReflectLE R], a ≤ 0 → b ≤ 0 → (0 ≤ a * b) = True | false |
Lean.Parser.ParserExtension.Entry.category.sizeOf_spec | Lean.Parser.Extension | ∀ (catName declName : Lean.Name) (behavior : Lean.Parser.LeadingIdentBehavior),
sizeOf (Lean.Parser.ParserExtension.Entry.category catName declName behavior) =
1 + sizeOf catName + sizeOf declName + sizeOf behavior | true |
Std.Tactic.BVDecide.BVExpr.Cache.Key.w | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | Std.Tactic.BVDecide.BVExpr.Cache.Key → ℕ | true |
CategoryTheory.MorphismProperty.Over.pullbackComp._proof_2 | Mathlib.CategoryTheory.MorphismProperty.OverAdjunction | ∀ {T : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} T] {P Q : CategoryTheory.MorphismProperty T}
[inst_1 : Q.IsMultiplicative] {X Y Z : T} (f : X ⟶ Y) (g : Y ⟶ Z) [inst_2 : P.IsStableUnderBaseChangeAlong f]
[inst_3 : P.IsStableUnderBaseChangeAlong g] [inst_4 : P.HasPullbacksAlong f] [inst_5 : P.HasPullbacks... | false |
Set.MapsTo.vadd_set | Mathlib.GroupTheory.GroupAction.Pointwise | ∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} {F : Type u_4} [inst : VAdd M α] [inst_1 : VAdd M β]
[inst_2 : FunLike F α β] [AddActionHomClass F M α β] {f : F} {s : Set α} {t : Set β},
Set.MapsTo (⇑f) s t → ∀ (c : M), Set.MapsTo (⇑f) (c +ᵥ s) (c +ᵥ t) | true |
Codisjoint.map | Mathlib.Order.Hom.BoundedLattice | ∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Lattice α] [inst_1 : Lattice β] [inst_2 : FunLike F α β]
[inst_3 : OrderTop α] [inst_4 : OrderTop β] [TopHomClass F α β] [SupHomClass F α β] {a b : α} (f : F),
Codisjoint a b → Codisjoint (f a) (f b) | true |
NonUnitalStarSubalgebra.map | Mathlib.Algebra.Star.NonUnitalSubalgebra | {F : Type v'} →
{R : Type u} →
{A : Type v} →
{B : Type w} →
[inst : CommSemiring R] →
[inst_1 : NonUnitalNonAssocSemiring A] →
[inst_2 : Module R A] →
[inst_3 : Star A] →
[inst_4 : NonUnitalNonAssocSemiring B] →
[inst_5 : Module ... | true |
PrimeSpectrum.instNonemptyOfNontrivial | Mathlib.RingTheory.Spectrum.Prime.Basic | ∀ {R : Type u} [inst : CommSemiring R] [Nontrivial R], Nonempty (PrimeSpectrum R) | true |
Real.Angle.sign_two_nsmul_eq_neg_sign_iff | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | ∀ {θ : Real.Angle}, (2 • θ).sign = -θ.sign ↔ θ = 0 ∨ Real.pi / 2 < |θ.toReal| | true |
List.Perm.eq_reverse_of_sortedLE_of_sortedGE | Mathlib.Data.List.Sort | ∀ {α : Type u_1} [inst : PartialOrder α] {l₁ l₂ : List α}, l₁.Perm l₂ → l₁.SortedLE → l₂.SortedGE → l₁ = l₂.reverse | true |
nonempty_linearEquiv_of_lift_rank_eq | Mathlib.LinearAlgebra.Dimension.Free | ∀ {R : Type u} {M : Type v} {M' : Type v'} [inst : Semiring R] [StrongRankCondition R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] [Module.Free R M] [inst_5 : AddCommMonoid M'] [inst_6 : Module R M'] [Module.Free R M'],
Cardinal.lift.{v', v} (Module.rank R M) = Cardinal.lift.{v, v'} (Module.rank R M') → Nonemp... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_316 | Mathlib.GroupTheory.Perm.Cycle.Type | ∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α) (h_3 : ¬[g a, g (g a)].Nodup) (w_1 : α)
(h_5 : 2 ≤ List.count w_1 [g a, g (g a)]),
List.idxOfNth w_1 [g a, g (g a)] (List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)])[1] + 1 ≤
(List.filter (fun x => decide (x = w_1)) [g a, g ... | false |
Matrix.isSymm_transpose_iff | Mathlib.LinearAlgebra.Matrix.Symmetric | ∀ {α : Type u_1} {n : Type u_3} {A : Matrix n n α}, A.transpose.IsSymm ↔ A.IsSymm | true |
PointwiseConvergenceCLM.coeLMₛₗ | Mathlib.Topology.Algebra.Module.PointwiseConvergence | {𝕜₁ : Type u_4} →
{𝕜₂ : Type u_5} →
[inst : NormedField 𝕜₁] →
[inst_1 : NormedField 𝕜₂] →
(σ : 𝕜₁ →+* 𝕜₂) →
(E : Type u_7) →
(F : Type u_8) →
[inst_2 : AddCommGroup E] →
[inst_3 : TopologicalSpace E] →
[inst_4 : AddCommGroup... | true |
CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit._autoParam | Mathlib.CategoryTheory.Adjunction.Basic | Lean.Syntax | false |
Real.cosPartialEquiv._proof_5 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | ∀ θ ∈ Set.Icc 0 Real.pi, θ ≤ Real.pi | false |
AddSubgroup.relIndex_eq_one._simp_1 | Mathlib.GroupTheory.Index | ∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, (H.relIndex K = 1) = (K ≤ H) | false |
AlgebraicGeometry.Scheme.Hom | Mathlib.AlgebraicGeometry.Scheme | AlgebraicGeometry.Scheme → AlgebraicGeometry.Scheme → Type u_1 | true |
AdicCompletion.map_of | Mathlib.RingTheory.AdicCompletion.Functoriality | ∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{N : Type u_3} [inst_3 : AddCommGroup N] [inst_4 : Module R N] (f : M →ₗ[R] N) (x : M),
(AdicCompletion.map I f) ((AdicCompletion.of I M) x) = (AdicCompletion.of I N) (f x) | true |
Std.DTreeMap.toList_rci | Std.Data.DTreeMap.Slice | ∀ {α : Type u} {β : α → Type v} (cmp : autoParam (α → α → Ordering) Std.DTreeMap.toList_rci._auto_1) [Std.TransCmp cmp]
{t : Std.DTreeMap α β cmp} {bound : α},
Std.Slice.toList (Std.Rci.Sliceable.mkSlice t bound...*) = List.filter (fun e => (cmp e.fst bound).isGE) t.toList | true |
ContMDiff.smul | 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] {n : WithTop ℕ∞} {V : Type u_12}
[ins... | true |
LinearMap.lift_rank_le_of_surjective | Mathlib.LinearAlgebra.Dimension.Basic | ∀ {R : Type u} {M : Type v} {M' : Type v'} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid M'] [inst_4 : Module R M'] (f : M →ₗ[R] M'),
Function.Surjective ⇑f → Cardinal.lift.{v, v'} (Module.rank R M') ≤ Cardinal.lift.{v', v} (Module.rank R M) | true |
NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates._proof_3 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | ∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
Function.Injective (Quotient.lift (NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates K) ⋯) ∧
Function.Surjective (Quotient.lift (NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates K) ⋯) | false |
fwdDiff_aux.fwdDiffₗ_apply | Mathlib.Algebra.Group.ForwardDiff | ∀ (M : Type u_1) (G : Type u_2) [inst : AddCommMonoid M] [inst_1 : AddCommGroup G] (h : M) (f : M → G) (a : M),
(fwdDiff_aux.fwdDiffₗ M G h) f a = fwdDiff h f a | true |
_private.Mathlib.Topology.ContinuousOn.0.continuous_prod_of_discrete_left._simp_1_1 | Mathlib.Topology.ContinuousOn | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
Continuous f = ContinuousOn f Set.univ | false |
CategoryTheory.Pseudofunctor.mapComp'_hom_comp_mapComp'_hom_whiskerRight | Mathlib.CategoryTheory.Bicategory.Strict.Pseudofunctor | ∀ {B : Type u₁} {C : Type u₂} [inst : CategoryTheory.Bicategory B] [inst_1 : CategoryTheory.Bicategory.Strict B]
[inst_2 : CategoryTheory.Bicategory C] (F : CategoryTheory.Pseudofunctor B C) {b₀ b₁ b₂ b₃ : B} (f₀₁ : b₀ ⟶ b₁)
(f₁₂ : b₁ ⟶ b₂) (f₂₃ : b₂ ⟶ b₃) (f₀₂ : b₀ ⟶ b₂) (f₁₃ : b₁ ⟶ b₃) (f : b₀ ⟶ b₃)
(h₀₂ : Cate... | true |
ENat.lt_top_of_sum_ne_top | Mathlib.Data.ENat.BigOperators | ∀ {α : Type u_1} {s : Finset α} {f : α → ℕ∞}, ∑ x ∈ s, f x ≠ ⊤ → ∀ {a : α}, a ∈ s → f a < ⊤ | true |
UnitalShelf.act_self_act_eq | Mathlib.Algebra.Quandle | ∀ {S : Type u_1} [inst : UnitalShelf S] (x y : S), Shelf.act x (Shelf.act x y) = Shelf.act x y | true |
_private.Mathlib.MeasureTheory.SpecificCodomains.WithLp.0.MeasureTheory.memLp_piLp_iff._simp_1_1 | Mathlib.MeasureTheory.SpecificCodomains.WithLp | ∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {p : ENNReal} {ι : Type u_2} [inst : Fintype ι]
{E : ι → Type u_3} [inst_1 : (i : ι) → NormedAddCommGroup (E i)] {f : X → (i : ι) → E i},
(∀ (i : ι), MeasureTheory.MemLp (fun x => f x i) p μ) = MeasureTheory.MemLp f p μ | false |
SemiNormedGrp₁.of | Mathlib.Analysis.Normed.Group.SemiNormedGrp | (carrier : Type u) → [str : SeminormedAddCommGroup carrier] → SemiNormedGrp₁ | true |
MvPowerSeries.map._proof_7 | Mathlib.RingTheory.MvPowerSeries.Basic | ∀ {σ : Type u_1} {R : Type u_2} {S : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S)
(φ ψ : MvPowerSeries σ R),
(fun n => f ((MvPowerSeries.coeff n) (φ + ψ))) =
(fun n => f ((MvPowerSeries.coeff n) φ)) + fun n => f ((MvPowerSeries.coeff n) ψ) | false |
_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_3 | Mathlib.Combinatorics.SimpleGraph.StronglyRegular | ∀ {α : Type u_4} (s : Set α) [inst : Fintype ↑s], Fintype.card ↑s = s.toFinset.card | false |
CompositionAsSet.card_boundaries_pos | Mathlib.Combinatorics.Enumerative.Composition | ∀ {n : ℕ} (c : CompositionAsSet n), 0 < c.boundaries.card | true |
Polynomial.roots_C_mul | Mathlib.Algebra.Polynomial.Roots | ∀ {R : Type u} {a : R} [inst : CommRing R] [inst_1 : IsDomain R] (p : Polynomial R),
a ≠ 0 → (Polynomial.C a * p).roots = p.roots | true |
SMulWithZero.compHom | Mathlib.Algebra.GroupWithZero.Action.Defs | {M₀ : Type u_2} →
{M₀' : Type u_3} →
(A : Type u_7) →
[inst : Zero M₀] →
[inst_1 : Zero A] → [SMulWithZero M₀ A] → [inst_3 : Zero M₀'] → ZeroHom M₀' M₀ → SMulWithZero M₀' A | true |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Log.0.Complex.expOpenPartialHomeomorph._simp_3 | Mathlib.Analysis.SpecialFunctions.Complex.Log | ∀ {α : Type u} {a : α} {p : α → Prop}, (a ∈ {x | p x}) = p a | false |
Con.instCompleteLattice._proof_2 | Mathlib.GroupTheory.Congruence.Defs | ∀ {M : Type u_1} [inst : Mul M] (s : Set (Con M)), sInf s ∈ lowerBounds s ∧ sInf s ∈ upperBounds (lowerBounds s) | false |
NumberField.InfinitePlace.liesOver_conjugate_embedding_of_mem_ramifiedPlacesOver | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | ∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
{v : NumberField.InfinitePlace K} {w : NumberField.InfinitePlace L},
w ∈ NumberField.InfinitePlace.ramifiedPlacesOver L v →
NumberField.ComplexEmbedding.LiesOver (NumberField.ComplexEmbedding.conjugate w.embedding) v.embe... | true |
CategoryTheory.StrictPseudofunctor.comp_obj | Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor | ∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C] {D : Type u₃}
[inst_2 : CategoryTheory.Bicategory D] (F : CategoryTheory.StrictPseudofunctor B C)
(G : CategoryTheory.StrictPseudofunctor C D) (X : B), (F.comp G).obj X = G.obj (F.obj X) | true |
IsTopologicalAddGroup.toHSpace._proof_5 | Mathlib.Topology.Homotopy.HSpaces | ∀ (M : Type u_1) [inst : AddZeroClass M] [inst_1 : TopologicalSpace M] [inst_2 : ContinuousAdd M],
{ toFun := Function.uncurry Add.add, continuous_toFun := ⋯ }.comp
((ContinuousMap.const M 0).prodMk (ContinuousMap.id M)) =
{ toFun := Function.uncurry Add.add, continuous_toFun := ⋯ }.comp
((ContinuousM... | false |
Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_ite | Mathlib.RingTheory.Lasker | ∀ {R : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Submodule R M}
(s₀ : Finset ↑N.associatedPrimes),
IsLowerSet ↑s₀ →
∀ (q : Submodule R M),
q.IsPrimary →
∀ (p : ↑N.associatedPrimes),
(q.colon Set.univ).radical = ↑p →
Sub... | true |
Finmap.keys_singleton | Mathlib.Data.Finmap | ∀ {α : Type u} {β : α → Type v} (a : α) (b : β a), (Finmap.singleton a b).keys = {a} | true |
Std.TreeMap.mk.injEq | Std.Data.TreeMap.Basic | ∀ {α : Type u} {β : Type v} {cmp : autoParam (α → α → Ordering) Std.TreeMap._auto_1}
(inner inner_1 : Std.DTreeMap α (fun x => β) cmp), ({ inner := inner } = { inner := inner_1 }) = (inner = inner_1) | true |
OpenPartialHomeomorph.extend_preimage_mem_nhdsWithin | Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | ∀ {𝕜 : Type u_1} {E : Type u_2} {M : Type u_3} {H : Type u_4} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] [inst_4 : TopologicalSpace M]
(f : OpenPartialHomeomorph M H) {I : ModelWithCorners 𝕜 E H} {s t : Set M} {x : M},
x ∈ f.sour... | true |
_private.Mathlib.Algebra.Order.Archimedean.Basic.0.WithBot.instArchimedean._simp_1 | Mathlib.Algebra.Order.Archimedean.Basic | ∀ {α : Type u} [inst : AddMonoid α] (a : α) (n : ℕ), n • ↑a = ↑(n • a) | false |
Algebra.TensorProduct.mapOfCompatibleSMul._proof_7 | Mathlib.RingTheory.TensorProduct.Maps | ∀ (R : Type u_4) (S : Type u_1) (T : Type u_5) (A : Type u_2) (B : Type u_3) [inst : CommSemiring R]
[inst_1 : CommSemiring S] [inst_2 : CommSemiring T] [inst_3 : Semiring A] [inst_4 : Semiring B] [inst_5 : Algebra R A]
[inst_6 : Algebra R B] [inst_7 : Algebra S A] [inst_8 : Algebra S B] [inst_9 : Algebra T A]
[i... | false |
CategoryTheory.MonoidalCategory.selRightfAction._proof_11 | Mathlib.CategoryTheory.Monoidal.Action.Basic | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C] {d d' : C}
(f : d ⟶ d'),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor d).hom f =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.wh... | false |
LinearIsometry.map_sub | Mathlib.Analysis.Normed.Operator.LinearIsometry | ∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
{σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup E₂] [inst_4 : Module R E]
[inst_5 : Module R₂ E₂] (f : E →ₛₗᵢ[σ₁₂] E₂) (x y : E), f (x - y) = f x - f y | true |
TwoSidedIdeal.rightModule | Mathlib.RingTheory.TwoSidedIdeal.Operations | {R : Type u_1} → [inst : Ring R] → (I : TwoSidedIdeal R) → Module Rᵐᵒᵖ ↥I | true |
Fintype.linearCombination._proof_3 | Mathlib.LinearAlgebra.Finsupp.LinearCombination | ∀ {α : Type u_2} {M : Type u_1} (R : Type u_3) [inst : Fintype α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] (v : α → M) (f g : α → R), ∑ i, (f + g) i • v i = ∑ i, f i • v i + ∑ i, g i • v i | false |
Homeomorph.toOpenPartialHomeomorphOfImageEq._proof_2 | Mathlib.Topology.OpenPartialHomeomorph.Defs | ∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (e : X ≃ₜ Y) (s : Set X)
(t : Set Y) (h : ⇑e '' s = t), ContinuousOn (⇑e) (e.toPartialEquivOfImageEq s t h).source | false |
Projectivization.independent_iff_iSupIndep | Mathlib.LinearAlgebra.Projectivization.Independence | ∀ {ι : Type u_1} {K : Type u_2} {V : Type u_3} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
{f : ι → Projectivization K V}, Projectivization.Independent f ↔ iSupIndep fun i => (f i).submodule | true |
_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_ge_two_eq_self._proof_1_2 | Mathlib.Data.Nat.Hyperoperation | ∀ (m n : ℕ), hyperoperation (n + 2) m 1 = m → hyperoperation (n + 1 + 2) m 1 = m | false |
norm_eq_zero._simp_1 | Mathlib.Analysis.Normed.Group.Basic | ∀ {E : Type u_5} [inst : NormedAddGroup E] {a : E}, (‖a‖ = 0) = (a = 0) | false |
MvPolynomial.rTensorAlgEquiv.eq_1 | Mathlib.RingTheory.TensorProduct.MvPolynomial | ∀ {R : Type u} {N : Type v} [inst : CommSemiring R] {σ : Type u_1} {S : Type u_3} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [inst_3 : CommSemiring N] [inst_4 : Algebra R N] [inst_5 : DecidableEq σ],
MvPolynomial.rTensorAlgEquiv = AlgEquiv.ofLinearEquiv MvPolynomial.rTensor ⋯ ⋯ | true |
ContinuousAlternatingMap.instTopologicalSpace | Mathlib.Topology.Algebra.Module.Alternating.Topology | {𝕜 : Type u_1} →
{E : Type u_2} →
{F : Type u_3} →
{ι : Type u_4} →
[inst : NormedField 𝕜] →
[inst_1 : AddCommGroup E] →
[inst_2 : Module 𝕜 E] →
[inst_3 : TopologicalSpace E] →
[inst_4 : AddCommGroup F] →
[inst_5 : Module 𝕜 F]... | true |
LeanSearchClient.unicode_turnstile | LeanSearchClient.LoogleSyntax | Lean.Parser.Parser | true |
DomMulAct.instMulDistribMulActionMonoidHom._proof_2 | Mathlib.GroupTheory.GroupAction.DomAct.Basic | ∀ {A : Type u_2} {M : Type u_1} {B : Type u_3} [inst : Monoid M] [inst_1 : Monoid A] [inst_2 : MulDistribMulAction M A]
[inst_3 : CommMonoid B] (x : Mᵈᵐᵃ) (x_1 : A →* B), (MonoidHom.coeFn A B) (x • x_1) = (MonoidHom.coeFn A B) (x • x_1) | false |
Disjoint.of_preimage | Mathlib.Data.Set.Image | ∀ {α : Type u_1} {β : Type u_2} {f : α → β},
Function.Surjective f → ∀ {s t : Set β}, Disjoint (f ⁻¹' s) (f ⁻¹' t) → Disjoint s t | true |
CommRingCat.coyonedaUnique_inv_app_hom_apply | Mathlib.Algebra.Category.Ring.Adjunctions | ∀ {n : Type v} [inst : Unique n] (X : CommRingCat) (a : ↑X) (a_1 : Opposite.unop (Opposite.op n)),
(CommRingCat.Hom.hom (CommRingCat.coyonedaUnique.inv.app X)) a a_1 = a | true |
Int.emod_eq_zero_of_dvd | Init.Data.Int.DivMod.Bootstrap | ∀ {a b : ℤ}, a ∣ b → b % a = 0 | true |
Lean.Meta.SynthInstance.TableEntry.mk.injEq | Lean.Meta.SynthInstance | ∀ (waiters : Array Lean.Meta.SynthInstance.Waiter) (answers : Array Lean.Meta.SynthInstance.Answer)
(waiters_1 : Array Lean.Meta.SynthInstance.Waiter) (answers_1 : Array Lean.Meta.SynthInstance.Answer),
({ waiters := waiters, answers := answers } = { waiters := waiters_1, answers := answers_1 }) =
(waiters = wa... | true |
FirstOrder.Language.BoundedFormula.realize_iAlls._simp_1 | Mathlib.ModelTheory.Semantics | ∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {β : Type v'} [inst_1 : Finite β]
{φ : L.Formula (α ⊕ β)} {v : α → M} {v' : Fin 0 → M},
FirstOrder.Language.BoundedFormula.Realize (FirstOrder.Language.Formula.iAlls β φ) v v' =
∀ (i : β → M), φ.Realize fun a => Sum.elim v i a | false |
_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.digitsAux0.match_1.eq_1 | Mathlib.Data.Nat.Digits.Defs | ∀ (motive : ℕ → Sort u_1) (h_1 : Unit → motive 0) (h_2 : (n : ℕ) → motive n.succ),
(match 0 with
| 0 => h_1 ()
| n.succ => h_2 n) =
h_1 () | true |
SemimoduleCat.coe_of | Mathlib.Algebra.Category.ModuleCat.Semi | ∀ (R : Type u) [inst : Semiring R] (X : Type v) [inst_1 : Semiring X] [inst_2 : Module R X], ↑(SemimoduleCat.of R X) = X | true |
Localization.lt._proof_2 | Mathlib.GroupTheory.MonoidLocalization.Order | ∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelMonoid α] {s : Submonoid α} {a₁ b₁ : α}
{a₂ b₂ : ↥s} {c₁ d₁ : α} {c₂ d₂ : ↥s},
(Localization.r s) (a₁, a₂) (b₁, b₂) →
(Localization.r s) (c₁, c₂) (d₁, d₂) → (↑c₂ * a₁ < ↑a₂ * c₁) = (↑d₂ * b₁ < ↑b₂ * d₁) | false |
vsub_left_injective | Mathlib.Algebra.AddTorsor.Basic | ∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p : P), Function.Injective fun x => x -ᵥ p | true |
CategoryTheory.Limits.Types.Image.ι | Mathlib.CategoryTheory.Limits.Types.Images | {α β : Type u} → (f : α ⟶ β) → CategoryTheory.Limits.Types.Image f ⟶ β | true |
WeierstrassCurve.natDegree_Ψ₂Sq_le | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | ∀ {R : Type u} [inst : CommRing R] (W : WeierstrassCurve R), W.Ψ₂Sq.natDegree ≤ 3 | true |
Prod.seminormedRing._proof_14 | Mathlib.Analysis.Normed.Ring.Basic | ∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedRing α] [inst_1 : SeminormedRing β] (a : α × β),
SubNegMonoid.zsmul 0 a = 0 | false |
Complex.log_mul_ofReal | Mathlib.Analysis.SpecialFunctions.Complex.Log | ∀ (r : ℝ), 0 < r → ∀ (x : ℂ), x ≠ 0 → Complex.log (x * ↑r) = ↑(Real.log r) + Complex.log x | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.fastUmulOverflow._proof_1_1 | Init.Data.BitVec.Bitblast | ∀ (x : BitVec (0 + 1)), ¬x.toNat ≤ 1 → False | false |
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