name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
Matrix.toBilin' | Mathlib.LinearAlgebra.Matrix.BilinearForm | {R₁ : Type u_1} →
[inst : CommSemiring R₁] →
{n : Type u_5} → [Fintype n] → [DecidableEq n] → Matrix n n R₁ ≃ₗ[R₁] LinearMap.BilinForm R₁ (n → R₁) | true |
PowerSeries.coeff_expand_mul | Mathlib.RingTheory.PowerSeries.Expand | ∀ {R : Type u_2} [inst : CommRing R] (p : ℕ) (hp : p ≠ 0) (φ : PowerSeries R) (m : ℕ),
(PowerSeries.coeff (p * m)) ((PowerSeries.expand p hp) φ) = (PowerSeries.coeff m) φ | true |
Lean.Meta.TransparencyMode._sizeOf_1 | Init.MetaTypes | Lean.Meta.TransparencyMode → ℕ | false |
instAddCommGroupUniformOnFun.eq_1 | Mathlib.Topology.Algebra.UniformConvergence | ∀ {α : Type u_1} {β : Type u_2} {𝔖 : Set (Set α)} [inst : AddCommGroup β],
instAddCommGroupUniformOnFun = { toAddGroup := instAddGroupUniformOnFun, add_comm := ⋯ } | true |
Order.Ioo_succ_right_eq_insert | Mathlib.Order.SuccPred.Basic | ∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α],
a < b → Set.Ioo a (Order.succ b) = insert b (Set.Ioo a b) | true |
OrderIso.limsup_apply | Mathlib.Order.LiminfLimsup | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_6} [inst : ConditionallyCompleteLattice β]
[inst_1 : ConditionallyCompleteLattice γ] {f : Filter α} {u : α → β} (g : β ≃o γ),
autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) f u) OrderIso.limsup_apply._auto_1 →
autoParam (Filter.IsCoboundedUnder (fun x1 x2 => ... | true |
Stream'.WSeq.findIndexes.match_1 | Mathlib.Data.WSeq.Defs | {α : Type u_1} → (motive : α × ℕ → Sort u_2) → (x : α × ℕ) → ((a : α) → (n : ℕ) → motive (a, n)) → motive x | false |
Int.natAbs_natCast_sub_natCast_of_ge | Mathlib.Data.Int.NatAbs | ∀ {a b : ℕ}, b ≤ a → (↑a - ↑b).natAbs = a - b | true |
LinearMap.lcompₛₗ.eq_1 | Mathlib.LinearAlgebra.BilinearMap | ∀ {R : Type u_14} {R₂ : Type u_15} {R₃ : Type u_16} (R₅ : Type u_18) {M : Type u_19} {N : Type u_20} (P : Type u_21)
[inst : Semiring R] [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : Semiring R₅] {σ₁₂ : R →+* R₂}
(σ₂₃ : R₂ →+* R₃) {σ₁₃ : R →+* R₃} [inst_4 : AddCommMonoid M] [inst_5 : AddCommMonoid N] [ins... | true |
CategoryTheory.Limits.WalkingMulticospan.instSmallCategory._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | ∀ {J : CategoryTheory.Limits.MulticospanShape} {W X Y Z : CategoryTheory.Limits.WalkingMulticospan J} (f : W.Hom X)
(g : X.Hom Y) (h : Y.Hom Z), (f.comp g).comp h = f.comp (g.comp h) | false |
Subsemiring.topologicalClosure._proof_5 | Mathlib.Topology.Algebra.Ring.Basic | ∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : Semiring R] [inst_2 : IsSemitopologicalSemiring R]
(s : Subsemiring R) {a b : R},
a ∈ s.toAddSubmonoid.topologicalClosure.carrier →
b ∈ s.toAddSubmonoid.topologicalClosure.carrier → a + b ∈ s.toAddSubmonoid.topologicalClosure.carrier | false |
Mathlib.Linter.Style.lambdaSyntax.findLambdaSyntax | Mathlib.Tactic.Linter.Style | Lean.Syntax → Array Lean.Syntax | true |
Lean.Compiler.LCNF.Simp.CtorInfo.recOn | Lean.Compiler.LCNF.Simp.DiscrM | {motive : Lean.Compiler.LCNF.Simp.CtorInfo → Sort u} →
(t : Lean.Compiler.LCNF.Simp.CtorInfo) →
((val : Lean.ConstructorVal) →
(args : Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Purity.pure)) →
motive (Lean.Compiler.LCNF.Simp.CtorInfo.ctor val args)) →
((n : ℕ) → motive (Lean.Compile... | false |
Lean.Elab.Do.elabDoTry._regBuiltin.Lean.Elab.Do.elabDoTry_1 | Lean.Elab.BuiltinDo.TryCatch | IO Unit | false |
Bool.not_bijective | Mathlib.Logic.Equiv.Bool | Function.Bijective not | true |
ContinuousLinearMap.rangeRestrict._proof_1 | Mathlib.Topology.Algebra.Module.LinearMap | ∀ {R₁ : Type u_3} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] {σ₁₂ : R₁ →+* R₂} {M₁ : Type u_4}
[inst_2 : TopologicalSpace M₁] [inst_3 : AddCommMonoid M₁] {M₂ : Type u_1} [inst_4 : TopologicalSpace M₂]
[inst_5 : AddCommMonoid M₂] [inst_6 : Module R₁ M₁] [inst_7 : Module R₂ M₂] [inst_8 : RingHomSurje... | false |
CategoryTheory.Limits.instDecidableEqWalkingParallelFamily._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers | ∀ {J : Type u_1}, CategoryTheory.Limits.WalkingParallelFamily.zero = CategoryTheory.Limits.WalkingParallelFamily.zero | false |
not_lt_of_ge | Mathlib.Order.Defs.PartialOrder | ∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a ≤ b → ¬b < a | true |
groupCohomology.cochainsMap_id_f_map_mono | Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | ∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {A B : Rep.{u, u, u} k G} (φ : A ⟶ B) [CategoryTheory.Mono φ]
(i : ℕ), CategoryTheory.Mono ((groupCohomology.cochainsMap (MonoidHom.id G) φ).f i) | true |
CochainComplex.isoHomologyπ₀._proof_1 | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(K : CochainComplex C ℕ), K.d ((ComplexShape.up ℕ).prev 0) 0 = 0 | false |
map_prod | Mathlib.Algebra.BigOperators.Group.Finset.Defs | ∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : CommMonoid M] [inst_1 : CommMonoid N] {G : Type u_7}
[inst_2 : FunLike G M N] [MonoidHomClass G M N] (g : G) (f : ι → M) (s : Finset ι),
g (∏ x ∈ s, f x) = ∏ x ∈ s, g (f x) | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.getMsbD_extractLsb._proof_1_2 | Init.Data.BitVec.Lemmas | ∀ {w hi lo i : ℕ},
i < hi - lo + 1 →
lo + (hi - lo + 1 - 1 - i) < w →
w - 1 - (lo + (hi - lo + 1 - 1 - i)) = w - 1 - (max hi lo - i) → ¬(i < hi - lo + 1 ∧ max hi lo - i < w) → False | false |
CochainComplex.shiftFunctorObjXIso.congr_simp | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
(K : CochainComplex C ℤ) (n i m : ℤ) (hm : m = i + n), K.shiftFunctorObjXIso n i m hm = K.shiftFunctorObjXIso n i m hm | true |
mabs_eq_max_inv | Mathlib.Algebra.Order.Group.Unbundled.Abs | ∀ {α : Type u_1} [inst : Group α] [inst_1 : LinearOrder α] {a : α}, |a|ₘ = max a a⁻¹ | true |
CategoryTheory.EffectiveEpi.casesOn | Mathlib.CategoryTheory.EffectiveEpi.Basic | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{X Y : C} →
{f : Y ⟶ X} →
{motive : CategoryTheory.EffectiveEpi f → Sort u} →
(t : CategoryTheory.EffectiveEpi f) →
((effectiveEpi : Nonempty (CategoryTheory.EffectiveEpiStruct f)) → motive ⋯) → motive t | false |
_private.Mathlib.Topology.Baire.Lemmas.0.Set.Finite.dense_sInter._simp_1_1 | Mathlib.Topology.Baire.Lemmas | ∀ {α : Type u_1} {P : α → Prop} {a : α} {s : Set α}, (∀ x ∈ insert a s, P x) = (P a ∧ ∀ x ∈ s, P x) | false |
Polynomial.degree.eq_1 | Mathlib.Algebra.Polynomial.Degree.Defs | ∀ {R : Type u} [inst : Semiring R] (p : Polynomial R), p.degree = p.support.max | true |
Tactic.ComputeAsymptotics.BasisExtension.insert.sizeOf_spec | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | ∀ {basis : Tactic.ComputeAsymptotics.Basis} (f : ℝ → ℝ) (ex : Tactic.ComputeAsymptotics.BasisExtension basis),
sizeOf (Tactic.ComputeAsymptotics.BasisExtension.insert f ex) = 1 + sizeOf basis + sizeOf ex | true |
Lean.Lsp.MarkupKind.ctorElim | Lean.Data.Lsp.Basic | {motive : Lean.Lsp.MarkupKind → Sort u} →
(ctorIdx : ℕ) → (t : Lean.Lsp.MarkupKind) → ctorIdx = t.ctorIdx → Lean.Lsp.MarkupKind.ctorElimType ctorIdx → motive t | false |
LieAlgebra.Orthogonal.indefiniteDiagonal_transform | Mathlib.Algebra.Lie.Classical | ∀ (p : Type u_2) (q : Type u_3) (R : Type u₂) [inst : DecidableEq p] [inst_1 : DecidableEq q] [inst_2 : CommRing R]
[inst_3 : Fintype p] [inst_4 : Fintype q] {i : R},
i * i = -1 →
(LieAlgebra.Orthogonal.Pso p q R i).transpose * LieAlgebra.Orthogonal.indefiniteDiagonal p q R *
LieAlgebra.Orthogonal.Pso p... | true |
Lean.Meta.DiscrTree.Key.proj.inj | Lean.Meta.DiscrTree.Types | ∀ {a : Lean.Name} {a_1 a_2 : ℕ} {a_3 : Lean.Name} {a_4 a_5 : ℕ},
Lean.Meta.DiscrTree.Key.proj a a_1 a_2 = Lean.Meta.DiscrTree.Key.proj a_3 a_4 a_5 → a = a_3 ∧ a_1 = a_4 ∧ a_2 = a_5 | true |
gcdMonoidOfLCM._proof_6 | Mathlib.Algebra.GCDMonoid.Basic | ∀ {α : Type u_1} [inst : CommMonoidWithZero α] (lcm : α → α → α), (∀ (a b : α), a ∣ lcm a b) → ∀ (x : α), lcm 0 x = 0 | false |
LinearEquiv.injective | Mathlib.Algebra.Module.Equiv.Defs | ∀ {R : Type u_1} {S : Type u_6} {M : Type u_7} {M₂ : Type u_9} [inst : Semiring R] [inst_1 : Semiring S]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_S_M₂ : Module S M₂}
{σ : R →+* S} {σ' : S →+* R} {re₁ : RingHomInvPair σ σ'} {re₂ : RingHomInvPair σ' σ} (e : M ≃ₛₗ[σ] M₂),
... | true |
CategoryTheory.Bicategory.LeftLift.alongId | Mathlib.CategoryTheory.Bicategory.Extension | {B : Type u} →
[inst : CategoryTheory.Bicategory B] →
{a c : B} → (g : c ⟶ a) → CategoryTheory.Bicategory.LeftLift (CategoryTheory.CategoryStruct.id a) g | true |
isSemilinearSet_iff | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | ∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsSemilinearSet s ↔ ∃ S, (∀ t ∈ S, IsLinearSet t) ∧ s = ⋃₀ ↑S | true |
Std.DTreeMap.Internal.Impl.Const.getEntryGT._sunfold | Std.Data.DTreeMap.Internal.Queries | {α : Type u} →
{β : Type v} →
[inst : Ord α] →
[Std.TransOrd α] →
(k : α) →
(t : Std.DTreeMap.Internal.Impl α fun x => β) → t.Ordered → (∃ a ∈ t, compare a k = Ordering.gt) → α × β | false |
Set.exists_mem_notMem_of_ncard_lt_ncard | Mathlib.Data.Set.Card | ∀ {α : Type u_1} {s t : Set α},
s.ncard < t.ncard → autoParam s.Finite Set.exists_mem_notMem_of_ncard_lt_ncard._auto_1 → ∃ e ∈ t, e ∉ s | true |
Finset.nonempty_Ioc._simp_1 | Mathlib.Order.Interval.Finset.Basic | ∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], (Finset.Ioc a b).Nonempty = (a < b) | false |
_private.Mathlib.Analysis.SpecialFunctions.Integrability.Basic.0.intervalIntegral.intervalIntegrable_inv_one_add_sq._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Integrability.Basic | ∀ {G : Type u_1} [inst : DivInvMonoid G] (a : G), a⁻¹ = 1 / a | false |
CategoryTheory.Functor.mapCochainComplexShiftIso._proof_1 | Mathlib.Algebra.Homology.HomotopyCategory.Shift | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.Preadditive C] {D : Type u_2}
[inst_2 : CategoryTheory.Category.{u_1, u_2} D] [inst_3 : CategoryTheory.Preadditive D]
(F : CategoryTheory.Functor C D) [inst_4 : F.Additive] (n : ℤ) (K : HomologicalComplex C (ComplexShape.up ℤ))
... | false |
Action.forget_δ | Mathlib.CategoryTheory.Action.Monoidal | ∀ {V : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} V] {G : Type u_2} [inst_1 : Monoid G]
[inst_2 : CategoryTheory.MonoidalCategory V] (X Y : Action V G),
CategoryTheory.Functor.OplaxMonoidal.δ (Action.forget V G) X Y =
CategoryTheory.CategoryStruct.id ((Action.forget V G).obj (CategoryTheory.MonoidalCa... | true |
ContinuousMonoidHom.instCoeOutOfMonoidHomClassOfContinuousMapClass | Mathlib.Topology.Algebra.ContinuousMonoidHom | {A : Type u_2} →
{B : Type u_3} →
[inst : Monoid A] →
[inst_1 : Monoid B] →
[inst_2 : TopologicalSpace A] →
[inst_3 : TopologicalSpace B] →
{F : Type u_7} →
[inst_4 : FunLike F A B] → [MonoidHomClass F A B] → [ContinuousMapClass F A B] → CoeOut F (A →ₜ* B) | true |
CategoryTheory.MorphismProperty.Over.isoMk._proof_3 | Mathlib.CategoryTheory.MorphismProperty.Comma | ∀ {T : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} T] {P Q : CategoryTheory.MorphismProperty T} {X : T}
{A B : P.Over Q X} (f : A.left ≅ B.left),
CategoryTheory.CategoryStruct.comp f.hom B.hom = A.hom →
CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id T).map f.hom) B.hom =
CategoryT... | false |
_private.Init.Data.Int.LemmasAux.0.Int.ble'_eq_true._proof_1_4 | Init.Data.Int.LemmasAux | ∀ (a a_1 : ℕ), ¬(a_1 ≤ a ↔ Int.negSucc a ≤ Int.negSucc a_1) → False | false |
Std.TreeMap.getKeyD_minKey? | Std.Data.TreeMap.Lemmas | ∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [Std.TransCmp cmp] {km fallback : α},
t.minKey? = some km → t.getKeyD km fallback = km | true |
ZMod.valMinAbs_natAbs_eq_min | Mathlib.Data.ZMod.ValMinAbs | ∀ {n : ℕ} [hpos : NeZero n] (a : ZMod n), a.valMinAbs.natAbs = min a.val (n - a.val) | true |
List.Sorted.decide | Mathlib.Data.List.Pairwise | ∀ {α : Type u_1} {R : α → α → Prop} [inst : DecidableRel R] (l : List α),
List.Pairwise R l → List.Pairwise (fun a b => decide (R a b) = true) l | true |
Std.HashMap.isEmpty_inter_right | Std.Data.HashMap.Lemmas | ∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {β : Type v} {m₁ m₂ : Std.HashMap α β} [EquivBEq α] [LawfulHashable α],
m₂.isEmpty = true → (m₁ ∩ m₂).isEmpty = true | true |
Lean.getAttrParamOptPrio | Lean.Attributes | Lean.Syntax → Lean.AttrM ℕ | true |
CategoryTheory.Preadditive.mono_iff_injective | Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
[inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
[inst_3 : CategoryTheory.HasForget₂ C Ab] [inst_4 : CategoryTheory.Preadditive C]
[inst_5 : (CategoryTheory.forge... | true |
ArchimedeanClass.FiniteElement._proof_2 | Mathlib.Algebra.Order.Ring.StandardPart | ∀ (K : Type u_1) [inst : LinearOrder K] [inst_1 : Field K] [IsOrderedRing K], IsStrictOrderedRing K | false |
CategoryTheory.HasDetector.casesOn | Mathlib.CategoryTheory.Generator.Basic | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{motive : CategoryTheory.HasDetector C → Sort u} →
(t : CategoryTheory.HasDetector C) → ((hasDetector : ∃ G, CategoryTheory.IsDetector G) → motive ⋯) → motive t | false |
isIrreducible_iff_sInter | Mathlib.Topology.Irreducible | ∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X},
IsIrreducible s ↔ ∀ (U : Finset (Set X)), (∀ u ∈ U, IsOpen u) → (∀ u ∈ U, (s ∩ u).Nonempty) → (s ∩ ⋂₀ ↑U).Nonempty | true |
derivWithin_const_smul | Mathlib.Analysis.Calculus.Deriv.Mul | ∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜} {R : Type u_2} [inst_3 : Monoid R]
[inst_4 : DistribMulAction R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F] (c : R),
DifferentiableWithinAt 𝕜 f s... | true |
TendstoLocallyUniformlyOn.comp | Mathlib.Topology.UniformSpace.LocallyUniformConvergence | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ι : Type u_4} [inst : TopologicalSpace α] [inst_1 : UniformSpace β]
{F : ι → α → β} {f : α → β} {s : Set α} {p : Filter ι} [inst_2 : TopologicalSpace γ] {t : Set γ},
TendstoLocallyUniformlyOn F f p s →
∀ (g : γ → α), Set.MapsTo g t s → ContinuousOn g t → TendstoLo... | true |
Hyperreal.instField._proof_7 | Mathlib.Analysis.Real.Hyperreal | ∀ (a : ℝ*), a + 0 = a | false |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toArray_roc_add_succ_right_eq_push._proof_1_1 | Init.Data.Range.Polymorphic.NatLemmas | ∀ {m n : ℕ}, ¬m ≤ m + n → False | false |
Lean.KeyedDeclsAttribute.AttributeEntry.ctorIdx | Lean.KeyedDeclsAttribute | {γ : Type} → Lean.KeyedDeclsAttribute.AttributeEntry γ → ℕ | false |
CategoryTheory.Pretriangulated.Opposite.rotateTriangleOpEquivalenceInverseObjRotateUnopIso._proof_4 | Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.HasShift C ℤ]
[inst_2 : CategoryTheory.Preadditive C] [∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive]
(T : CategoryTheory.Pretriangulated.Triangle Cᵒᵖ),
CategoryTheory.CategoryStruct.comp
(Opposite.unop ((Categor... | false |
_private.Mathlib.RingTheory.KrullDimension.Regular.0.ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson._simp_1_1 | Mathlib.RingTheory.KrullDimension.Regular | ∀ {R : Type u} {M : Type v} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (r : R)
(N : Submodule R M), r • N = Ideal.span {r} • N | false |
Metric.Snowflaking.instT2Space | Mathlib.Topology.MetricSpace.Snowflaking | ∀ {X : Type u_1} {α : ℝ} {hα₀ : 0 < α} {hα₁ : α ≤ 1} [inst : TopologicalSpace X] [T2Space X],
T2Space (Metric.Snowflaking X α hα₀ hα₁) | true |
LinearMap.BilinMap.tmul | Mathlib.LinearAlgebra.BilinearForm.TensorProduct | {R : Type uR} →
{A : Type uA} →
{M₁ : Type uM₁} →
{M₂ : Type uM₂} →
{N₁ : Type uN₁} →
{N₂ : Type uN₂} →
[inst : CommSemiring R] →
[inst_1 : CommSemiring A] →
[inst_2 : AddCommMonoid M₁] →
[inst_3 : AddCommMonoid M₂] →
... | true |
ENNReal.toNNReal_natCast_eq_toNNReal | Mathlib.Data.ENNReal.Basic | ∀ (n : ℕ), (↑n).toNNReal = (↑n).toNNReal | true |
Cardinal.lift_eq_zero | Mathlib.SetTheory.Cardinal.Order | ∀ {a : Cardinal.{v}}, Cardinal.lift.{u, v} a = 0 ↔ a = 0 | true |
ContinuousMap.Homotopy.mk.inj | Mathlib.Topology.Homotopy.Basic | ∀ {X : Type u} {Y : Type v} {inst : TopologicalSpace X} {inst_1 : TopologicalSpace Y} {f₀ f₁ : C(X, Y)}
{toContinuousMap : C(↑unitInterval × X, Y)} {map_zero_left : ∀ (x : X), toContinuousMap.toFun (0, x) = f₀ x}
{map_one_left : ∀ (x : X), toContinuousMap.toFun (1, x) = f₁ x} {toContinuousMap_1 : C(↑unitInterval × ... | true |
Lean.Omega.Coeffs.isZero | Init.Omega.Coeffs | Lean.Omega.Coeffs → Prop | true |
CartanMatrix.E₆.eq_1 | Mathlib.Data.Matrix.Cartan | CartanMatrix.E₆ =
!![2, 0, -1, 0, 0, 0;
0, 2, 0, -1, 0, 0;
-1, 0, 2, -1, 0, 0;
0, -1, -1, 2, -1, 0;
0, 0, 0, -1, 2, -1;
0, 0, 0, 0, -1, 2] | true |
Aesop.IndexMatchLocation.none.elim | Aesop.Index.Basic | {motive : Aesop.IndexMatchLocation → Sort u} →
(t : Aesop.IndexMatchLocation) → t.ctorIdx = 0 → motive Aesop.IndexMatchLocation.none → motive t | false |
CategoryTheory.ComposableArrows.threeδ₃Toδ₂.congr_simp | Mathlib.Algebra.Homology.SpectralObject.Page | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {i j k l : C} (f₁ : i ⟶ j) (f₂ : j ⟶ k) (f₃ f₃_1 : k ⟶ l)
(e_f₃ : f₃ = f₃_1) (f₂₃ : j ⟶ l) (h₂₃ : CategoryTheory.CategoryStruct.comp f₂ f₃ = f₂₃),
CategoryTheory.ComposableArrows.threeδ₃Toδ₂ f₁ f₂ f₃ f₂₃ h₂₃ =
CategoryTheory.ComposableArrows.threeδ₃Toδ₂ f... | true |
Unitization.inrRangeEquiv._proof_1 | Mathlib.Algebra.Algebra.Unitization | ∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R] [inst_1 : StarAddMonoid R] [inst_2 : NonUnitalSemiring A]
[inst_3 : Star A] [inst_4 : Module R A], NonUnitalAlgHomClass (A →⋆ₙₐ[R] Unitization R A) R A (Unitization R A) | false |
Right.inv_le_self | Mathlib.Algebra.Order.Group.Unbundled.Basic | ∀ {α : Type u} [inst : Group α] [inst_1 : Preorder α] [MulRightMono α] {a : α}, 1 ≤ a → a⁻¹ ≤ a | true |
Batteries.RBMap.instForInValuesOfMonad | Batteries.Data.RBMap.Basic | {α : Type u} →
{β : Type v} →
{cmp : α → α → Ordering} → {m : Type u_1 → Type u_2} → [Monad m] → ForIn m (Batteries.RBMap.Values α β cmp) β | true |
Prod.smulZeroClass | Mathlib.Algebra.GroupWithZero.Action.Prod | {R : Type u_5} →
{M : Type u_6} →
{N : Type u_7} →
[inst : Zero M] → [inst_1 : Zero N] → [SMulZeroClass R M] → [SMulZeroClass R N] → SMulZeroClass R (M × N) | true |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.signVariations_eraseLead_mul_X_sub_C._proof_1_1 | Mathlib.Algebra.Polynomial.RuleOfSigns | ∀ {R : Type u_1} [inst : Ring R] {P : Polynomial R} {η : R} (d : ℕ),
P.natDegree = d + 1 →
((Polynomial.X - Polynomial.C η) * P).natDegree = P.natDegree + 1 →
((Polynomial.X - Polynomial.C η) * P).nextCoeff = P.coeff d - η * P.coeff (d + 1) | false |
IsPurelyInseparable.tower_bot | Mathlib.FieldTheory.PurelyInseparable.Basic | ∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K]
[inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K] [IsPurelyInseparable F K], IsPurelyInseparable F E | true |
CategoryTheory.Limits.image.lift_mk_factorThruImage_assoc | Mathlib.CategoryTheory.Limits.Shapes.Images | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y}
[inst_1 : CategoryTheory.Limits.HasImage f] {Z : C} (h : Y ⟶ Z),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.Limits.image.lift
{ I := CategoryTheory.Limits.image f, m := CategoryTheory.Limits.image.ι f, m_mono := ⋯,
... | true |
Lean.DataValue.recOn | Lean.Data.KVMap | {motive : Lean.DataValue → Sort u} →
(t : Lean.DataValue) →
((v : String) → motive (Lean.DataValue.ofString v)) →
((v : Bool) → motive (Lean.DataValue.ofBool v)) →
((v : Lean.Name) → motive (Lean.DataValue.ofName v)) →
((v : ℕ) → motive (Lean.DataValue.ofNat v)) →
((v : ℤ) → mo... | false |
Perfection.lift | Mathlib.RingTheory.Perfection | (p : ℕ) →
[hp : Fact (Nat.Prime p)] →
(R : Type u₁) →
[inst : CommSemiring R] →
[CharP R p] →
[PerfectRing R p] →
(S : Type u₂) → [inst_3 : CommSemiring S] → [inst_4 : CharP S p] → (R →+* S) ≃ (R →+* Perfection S p) | true |
Polynomial.instFree | Mathlib.LinearAlgebra.Finsupp.VectorSpace | ∀ {R : Type u_1} [inst : Semiring R], Module.Free R (Polynomial R) | true |
Lean.Elab.Frontend.State.ctorIdx | Lean.Elab.Frontend | Lean.Elab.Frontend.State → ℕ | false |
Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C | Mathlib.FieldTheory.Separable | ∀ {R : Type u} [inst : CommRing R] {n : ℕ} (a b c : R),
↑n = 0 → IsUnit b → (Polynomial.C a * Polynomial.X ^ n + Polynomial.C b * Polynomial.X + Polynomial.C c).Separable | true |
CategoryTheory.ShortComplex.π₂_map | Mathlib.Algebra.Homology.ShortComplex.Basic | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{X Y : CategoryTheory.ShortComplex C} (f : X ⟶ Y), CategoryTheory.ShortComplex.π₂.map f = f.τ₂ | true |
zpow_mod_orderOf | Mathlib.GroupTheory.OrderOfElement | ∀ {G : Type u_1} [inst : Group G] (x : G) (z : ℤ), x ^ (z % ↑(orderOf x)) = x ^ z | true |
Matrix.instNonAssocRing._proof_5 | Mathlib.Data.Matrix.Mul | ∀ {n : Type u_1} {α : Type u_2} [inst : DecidableEq n] [inst_1 : NonAssocRing α] (a : Matrix n n α), -a + a = 0 | false |
Nat.prod_mem_smoothNumbers | Mathlib.NumberTheory.SmoothNumbers | ∀ (n N : ℕ), (List.filter (fun x => decide (x < N)) n.primeFactorsList).prod ∈ N.smoothNumbers | true |
CategoryTheory.Functor.FullyFaithful.addMonObj._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.MonoidalCategory C]
{D : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} D] [inst_3 : CategoryTheory.MonoidalCategory D]
{F : CategoryTheory.Functor C D} [inst_4 : F.OplaxMonoidal] (hF : F.FullyFaithful) (X : C)
[inst_5... | false |
String.Pos.isUTF8FirstByte_getUTF8Byte_offset | Init.Data.String.Lemmas.Order | ∀ {s : String} {p : s.Pos} {h : p.offset < s.rawEndPos}, (s.getUTF8Byte p.offset h).IsUTF8FirstByte | true |
_private.Mathlib.Data.Finset.Sym.0.Finset.not_isDiag_mk_of_mem_offDiag._proof_1_1 | Mathlib.Data.Finset.Sym | ∀ {α : Type u_1} {s : Finset α} {a b : α}, a ∈ s ∧ b ∈ s ∧ ¬a = b → ¬a = b | false |
_private.Std.Time.Date.Unit.Year.0.Std.Time.Year.instReprEra.repr.match_1 | Std.Time.Date.Unit.Year | (motive : Std.Time.Year.Era → Sort u_1) →
(x : Std.Time.Year.Era) → (Unit → motive Std.Time.Year.Era.bce) → (Unit → motive Std.Time.Year.Era.ce) → motive x | false |
Filter.map_neg | Mathlib.Order.Filter.Pointwise | ∀ {α : Type u_2} [inst : Neg α] {f : Filter α}, Filter.map Neg.neg f = -f | true |
DirectLimit.instMulActionOfMulActionHomClass._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 : Monoid R]
... | false |
_private.Mathlib.Data.Seq.Parallel.0.Computation.parallel.aux1.match_1.eq_3 | Mathlib.Data.Seq.Parallel | ∀ {α : Type u_1} (motive : Option (Stream'.Seq1 (Option (Computation α))) → Sort u_2) (c : Computation α)
(S' : Stream'.Seq (Option (Computation α))) (h_1 : Unit → motive none)
(h_2 : (S' : Stream'.Seq (Option (Computation α))) → motive (some (none, S')))
(h_3 : (c : Computation α) → (S' : Stream'.Seq (Option (Co... | true |
Subsemiring.centralizer_eq_top_iff_subset | Mathlib.Algebra.Ring.Subsemiring.Basic | ∀ {R : Type u_1} [inst : Semiring R] {s : Set R}, Subsemiring.centralizer s = ⊤ ↔ s ⊆ ↑(Subsemiring.center R) | true |
CategoryTheory.Retract.trans._proof_2 | Mathlib.CategoryTheory.Retract | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} (h : CategoryTheory.Retract X Y) {Z : C}
(h' : CategoryTheory.Retract Y Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp h.i h'.i)
(CategoryTheory.CategoryStruct.comp h'.r h.r) =
CategoryTheory.CategoryStruc... | false |
VAdd.mk._flat_ctor | Mathlib.Algebra.Notation.Defs | {G : Type u} → {P : Type v} → (G → P → P) → VAdd G P | false |
Std.Rxc.LawfulHasSize.size_eq_succ_of_succ?_eq_some | Init.Data.Range.Polymorphic.Basic | ∀ {α : Type u} {inst : LE α} {inst_1 : Std.PRange.UpwardEnumerable α} {inst_2 : Std.Rxc.HasSize α}
[self : Std.Rxc.LawfulHasSize α] (lo hi lo' : α),
lo ≤ hi → Std.PRange.succ? lo = some lo' → Std.Rxc.HasSize.size lo hi = Std.Rxc.HasSize.size lo' hi + 1 | true |
right_eq_ite_iff | Init.PropLemmas | ∀ {α : Sort u_1} {p : Prop} [inst : Decidable p] {x y : α}, (y = if p then x else y) ↔ p → y = x | true |
isDedekindDomain_iff | Mathlib.RingTheory.DedekindDomain.Basic | ∀ (A : Type u_2) [inst : CommRing A] (K : Type u_4) [inst_1 : CommRing K] [inst_2 : Algebra A K] [IsFractionRing A K],
IsDedekindDomain A ↔
IsDomain A ∧ IsNoetherianRing A ∧ Ring.DimensionLEOne A ∧ ∀ {x : K}, IsIntegral A x → ∃ y, (algebraMap A K) y = x | true |
Lean.RBNode.fold._unsafe_rec | Lean.Data.RBMap | {α : Type u} → {β : α → Type v} → {σ : Type w} → (σ → (k : α) → β k → σ) → σ → Lean.RBNode α β → σ | false |
AddSubgroup.index_pi | Mathlib.GroupTheory.Index | ∀ {G : Type u_1} [inst : AddGroup G] {ι : Type u_3} [inst_1 : Fintype ι] (H : ι → AddSubgroup G),
(AddSubgroup.pi Set.univ H).index = ∏ i, (H i).index | true |
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