name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.42M | docString stringlengths 0 11.5k ⌀ | allowCompletion bool 2
classes |
|---|---|---|---|---|
_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_5 | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | ∀ {a b c : Prop}, (a ∧ b ∧ c) = (b ∧ a ∧ c) | null | false |
Set.Icc.coe_pow | Mathlib.Algebra.Order.Interval.Set.Instances | ∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R] (x : ↑(Set.Icc 0 1)) (n : ℕ),
↑(x ^ n) = ↑x ^ n | null | true |
CategoryTheory.ShortComplex.shortExact_of_iso | Mathlib.Algebra.Homology.ShortComplex.ShortExact | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (e : S₁ ≅ S₂), S₁.ShortExact → S₂.ShortExact | null | true |
_private.Init.Data.Nat.Basic.0.Nat.lt_trichotomy.match_1_3 | Init.Data.Nat.Basic | ∀ (a b : ℕ) (motive : a < b ∨ a ≥ b → Prop) (x : a < b ∨ a ≥ b),
(∀ (h : a < b), motive ⋯) → (∀ (h : a ≥ b), motive ⋯) → motive x | null | false |
SetLike.instSubtypeSet | Mathlib.Data.SetLike.Basic | {X : Type u_3} → {p : Set X → Prop} → SetLike { s // p s } X | membership is inherited from `Set X` | true |
Std.IterM.anyM_filterMapM | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | ∀ {α β β' : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [inst : Std.Iterator α m β]
[Std.Iterators.Finite α m] [inst_2 : MonadLiftT m n] [inst_3 : Monad m] [LawfulMonad m] [inst_5 : Monad n]
[inst_6 : MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] {it : Std.IterM m β} {f : β → n (Option β')}
... | null | true |
CategoryTheory.associativity_app_assoc | Mathlib.CategoryTheory.Monoidal.End | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {M : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} M]
[inst_2 : CategoryTheory.MonoidalCategory M] (F : CategoryTheory.Functor M (CategoryTheory.Functor C C))
(m₁ m₂ m₃ : M) (X : C) [inst_3 : F.LaxMonoidal] {Z : C}
(h :
(F.obj
(Cate... | null | true |
permsOfList._unsafe_rec | Mathlib.Data.Fintype.Perm | {α : Type u_1} → [DecidableEq α] → List α → List (Equiv.Perm α) | null | false |
Std.Do.SPred.Notation.unexpandIff | Std.Do.SPred.Notation | Lean.PrettyPrinter.Unexpander | Unexpander that reconstructs `spred(... ↔ ...)⌝` syntax from applications of `SPred.iff`, lifting
nested applications of `spred(...)` from the arguments.
| true |
_private.Init.Data.String.Basic.0.String.Pos.Raw.isValid_copy_iff._simp_1_6 | Init.Data.String.Basic | ∀ {s : String} {l r : s.Pos}, (l ≤ r) = (l.offset ≤ r.offset) | null | false |
WithAbs.algebraLeft | Mathlib.Analysis.Normed.Ring.WithAbs | {S : Type u_2} →
[inst : Semiring S] →
[inst_1 : PartialOrder S] →
{R : Type u_3} →
(T : Type u_4) →
[inst_2 : CommSemiring R] →
[inst_3 : Semiring T] → [Algebra R T] → (v : AbsoluteValue R S) → Algebra (WithAbs v) T | null | true |
MonoidAlgebra.coeff_zero | Mathlib.Algebra.MonoidAlgebra.Defs | ∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R], MonoidAlgebra.coeff 0 = 0 | null | true |
_private.Mathlib.Combinatorics.Quiver.Path.Vertices.0.Quiver.Path.verticesSet_nil._simp_1_2 | Mathlib.Combinatorics.Quiver.Path.Vertices | ∀ {α : Type u} {a b : Set α}, (a = b) = ∀ (x : α), x ∈ a ↔ x ∈ b | null | false |
CategoryTheory.Subgroupoid.Map.Arrows | Mathlib.CategoryTheory.Groupoid.Subgroupoid | {C : Type u} →
[inst : CategoryTheory.Groupoid C] →
{D : Type u_1} →
[inst_1 : CategoryTheory.Groupoid D] →
(φ : CategoryTheory.Functor C D) →
Function.Injective φ.obj → CategoryTheory.Subgroupoid C → (c d : D) → (c ⟶ d) → Prop | The family of arrows of the image of a subgroupoid under a functor injective on objects | true |
Std.instDecidableEqRic.decEq | Init.Data.Range.Polymorphic.PRange | {α : Type u_1} → [DecidableEq α] → (x x_1 : Std.Ric α) → Decidable (x = x_1) | null | true |
instNonUnitalCStarAlgebraSubtypeMemNonUnitalStarSubalgebraComplexElemental._proof_7 | Mathlib.Analysis.CStarAlgebra.Classes | ∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] (x : A), IsClosed ↑(NonUnitalStarAlgebra.elemental ℂ x) | null | false |
_private.Batteries.Data.Fin.Coding.0.Fin.encodeProd.match_1.eq_1 | Batteries.Data.Fin.Coding | ∀ {m n : ℕ} (motive : Fin m × Fin n → Sort u_1) (i : Fin m) (j : Fin n)
(h_1 : (i : Fin m) → (j : Fin n) → motive (i, j)),
(match (i, j) with
| (i, j) => h_1 i j) =
h_1 i j | null | true |
Nat.minSqFacAux._unary | Mathlib.Data.Nat.Squarefree | (_ : ℕ) ×' ℕ → Option ℕ | Assuming that `n` has no factors less than `k`, returns the smallest prime `p` such that
`p^2 ∣ n`. | false |
topToLocale_map | Mathlib.Topology.Category.Locale | ∀ {X Y : TopCat} (f : X ⟶ Y), topToLocale.map f = (Frm.ofHom (TopologicalSpace.Opens.comap (TopCat.Hom.hom f))).op | null | true |
Fin.succFunEquiv | Mathlib.Logic.Equiv.Fin.Basic | (α : Type u_1) → (n : ℕ) → (Fin (n + 1) → α) ≃ (Fin n → α) × α | `Fin (n + 1) → α` and `(Fin n → α) × α` are equivalent. | true |
ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self' | Mathlib.Probability.Independence.ZeroOne | ∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {m0 : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω}
{μα : MeasureTheory.Measure α},
(∀ᵐ (a : α) ∂μα, MeasureTheory.IsFiniteMeasure (κ a)) →
∀ {t : Set Ω}, ProbabilityTheory.Kernel.IndepSet t t κ μα → ∀ᵐ (a : α) ∂μα, (κ a) t = 0 ∨ (κ a) t = 1 | null | true |
NonUnitalSubring.ext | Mathlib.RingTheory.NonUnitalSubring.Defs | ∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {S T : NonUnitalSubring R}, (∀ (x : R), x ∈ S ↔ x ∈ T) → S = T | Two non-unital subrings are equal if they have the same elements. | true |
Finset.mulAntidiagonal.eq_1 | Mathlib.Data.Finset.MulAntidiagonal | ∀ {α : Type u_1} [inst : CommMonoid α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedCancelMonoid α] {s t : Set α}
(hs : s.IsPWO) (ht : t.IsPWO) (a : α), Finset.mulAntidiagonal hs ht a = ⋯.toFinset | null | true |
gc_coinduced_induced | Mathlib.Topology.Order | ∀ {α : Type u_1} {β : Type u_2} (f : α → β),
GaloisConnection (TopologicalSpace.coinduced f) (TopologicalSpace.induced f) | null | true |
_private.Mathlib.Data.Fin.Tuple.NatAntidiagonal.0.List.Nat.antidiagonalTuple_one._simp_1_7 | Mathlib.Data.Fin.Tuple.NatAntidiagonal | ∀ {α : Type u_1} {β : Type u_2} {f : α → β} {l : List α}, (List.map f l = []) = (l = []) | null | false |
Manifold.IsSubmersionAtOfComplement.instNormedSpaceSmallComplement._proof_1 | Mathlib.Geometry.Manifold.Submersion | ∀ {𝕜 : Type u_2} {E'' : Type u_3} {F : Type u_4} {H : Type u_5} {G : Type u_6} {E : Type u_1}
[inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
[inst_3 : NormedAddCommGroup E''] [inst_4 : NormedSpace 𝕜 E''] [inst_5 : NormedAddCommGroup F]
[inst_6 : NormedSpace 𝕜 F]... | null | false |
_private.Init.Data.UInt.Bitwise.0.UInt8.shiftLeft_zero._simp_1_1 | Init.Data.UInt.Bitwise | ∀ {a b : UInt8}, (a = b) = (a.toBitVec = b.toBitVec) | null | false |
Equiv.coe_fn_mk | Mathlib.Logic.Equiv.Defs | ∀ {α : Sort u} {β : Sort v} (f : α → β) (g : β → α) (l : Function.LeftInverse g f) (r : Function.RightInverse g f),
⇑{ toFun := f, invFun := g, left_inv := l, right_inv := r } = f | null | true |
MeromorphicOn.divisor_natCast | Mathlib.Analysis.Meromorphic.Divisor | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} (n : ℕ), MeromorphicOn.divisor (↑n) U = 0 | The divisor of a constant function is `0`.
| true |
CyclotomicField.instIsScalarTower._proof_1 | Mathlib.NumberTheory.Cyclotomic.Basic | ∀ (n : ℕ) (A : Type u_1) (K : Type u_2) [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K],
IsScalarTower A K (CyclotomicField n K) | null | false |
Subalgebra.op_iSup | Mathlib.Algebra.Algebra.Subalgebra.MulOpposite | ∀ {ι : Sort u_1} {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(S : ι → Subalgebra R A), (iSup S).op = ⨆ i, (S i).op | null | true |
Bool.or' | Init.Data.Bool | Bool → Bool → Bool | null | true |
CoxeterSystem.IsReflection.isLeftInversion_mul_right_iff | Mathlib.GroupTheory.Coxeter.Inversion | ∀ {B : Type u_1} {W : Type u_2} [inst : Group W] {M : CoxeterMatrix B} {cs : CoxeterSystem M W} {t : W},
cs.IsReflection t → ∀ {w : W}, cs.IsLeftInversion (t * w) t ↔ ¬cs.IsLeftInversion w t | null | true |
_private.Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence.0.CategoryTheory.Abelian.SpectralObject.HasSpectralSequence._proof_14 | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | ∀ {ι : Type u_1} {κ : Type u_2} [inst_2 : Preorder ι] {c : ℤ → ComplexShape κ} {r₀ : ℤ}
(data : CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore ι c r₀) (r r' : ℤ) (pq : κ)
(hrr' : r + -1 * r' + 1 = 0) (hr : r₀ + -1 * r ≤ 0), data.i₀ r' pq ⋯ ≤ data.i₀ r pq ⋯ | null | false |
CochainComplex.HomComplex.Cochain.rightShiftAddEquiv._proof_4 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
(K L : CochainComplex C ℤ) (n a n' : ℤ) (hn' : n' + a = n)
(γ : CochainComplex.HomComplex.Cochain K ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) a).obj L) n'),
(fun γ => γ.rightShift a n' hn') ((fun γ => γ... | null | false |
MeasureTheory.SimpleFunc.map_mul | Mathlib.MeasureTheory.Function.SimpleFunc | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : Mul β] [inst_2 : Mul γ] {g : β → γ},
(∀ (x y : β), g (x * y) = g x * g y) →
∀ (f₁ f₂ : MeasureTheory.SimpleFunc α β),
MeasureTheory.SimpleFunc.map g (f₁ * f₂) = MeasureTheory.SimpleFunc.map g f₁ * MeasureTheory.SimpleFunc.ma... | null | true |
WithTop.coe_mono | Mathlib.Order.WithBot | ∀ {α : Type u_1} [inst : Preorder α], Monotone fun a => ↑a | null | true |
CategoryTheory.Cat.freeMapIdIso_inv_app | Mathlib.CategoryTheory.Category.Quiv | ∀ (V : Type u_1) [inst : Quiver V] (X : CategoryTheory.Paths V),
(CategoryTheory.Cat.freeMapIdIso V).inv.app X = CategoryTheory.CategoryStruct.id X | null | true |
_private.Mathlib.Data.Setoid.Basic.0.Setoid.sSup_eq_eqvGen._simp_1_2 | Mathlib.Data.Setoid.Basic | ∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c) | null | false |
Submodule.FG.lTensor.directLimit.eq_1 | Mathlib.RingTheory.TensorProduct.DirectLimitFG | ∀ (R : Type u) (M : Type u_1) (N : Type u_2) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : DecidableEq { Q // Q.FG }],
Submodule.FG.lTensor.directLimit R M N =
(TensorProduct.directLimitRight (fun x x_1 => Submodule.inclusion)... | null | true |
Int8.toInt32_toInt64 | Init.Data.SInt.Lemmas | ∀ (n : Int8), n.toInt64.toInt32 = n.toInt32 | null | true |
Std.Http.instBEqVersion.beq | Std.Http.Data.Version | Std.Http.Version → Std.Http.Version → Bool | null | true |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.evalAlts.goWithIncremental.match_16 | Lean.Elab.Tactic.Induction | (motive : Option (Lean.MVarId × Lean.Meta.FVarSubst) → Sort u_1) →
(__x : Option (Lean.MVarId × Lean.Meta.FVarSubst)) →
((altMVarId' : Lean.MVarId) → (subst : Lean.Meta.FVarSubst) → motive (some (altMVarId', subst))) →
((x : Option (Lean.MVarId × Lean.Meta.FVarSubst)) → motive x) → motive __x | null | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.map_id_equiv._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {x : Ord α} {x_1 : BEq α} [Std.LawfulBEqOrd α] {a b : α}, (compare a b = Ordering.eq) = ((a == b) = true) | null | false |
Lean.Doc.Parser.listItem._unsafe_rec | Lean.DocString.Parser | Lean.Doc.Parser.BlockCtxt → Lean.Parser.ParserFn | null | false |
instLinearOrderEReal._aux_8 | Mathlib.Data.EReal.Basic | DecidableLE EReal | null | false |
_private.Mathlib.Data.QPF.Multivariate.Constructions.Cofix.0.Mathlib.Tactic.MvBisim._aux_Mathlib_Data_QPF_Multivariate_Constructions_Cofix___elabRules_Mathlib_Tactic_MvBisim_tacticMv_bisim___With____1.match_1 | Mathlib.Data.QPF.Multivariate.Constructions.Cofix | (motive : Option (Lean.TSyntax `Lean.binderIdent) → Sort u_1) →
(x : Option (Lean.TSyntax `Lean.binderIdent)) →
((s : Lean.TSyntax `Lean.binderIdent) → motive (some s)) → (Unit → motive none) → motive x | null | false |
Eq.to_iff | Init.Core | ∀ {a b : Prop}, a = b → (a ↔ b) | null | true |
Submodule.restrictScalars_traceDual | 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... | null | true |
Array.findSome?_map | Init.Data.Array.Find | ∀ {β : Type u_1} {γ : Type u_2} {α : Type u_3} {p : γ → Option α} {f : β → γ} {xs : Array β},
Array.findSome? p (Array.map f xs) = Array.findSome? (p ∘ f) xs | null | true |
AddMonoidHom.compHom._proof_1 | Mathlib.Algebra.Group.Hom.Instances | ∀ {M : Type u_1} {N : Type u_2} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddCommMonoid N]
[inst_2 : AddCommMonoid P], { toFun := AddMonoidHom.comp 0, map_zero' := ⋯, map_add' := ⋯ } = 0 | null | false |
Int16.and_assoc | Init.Data.SInt.Bitwise | ∀ (a b c : Int16), a &&& b &&& c = a &&& (b &&& c) | null | true |
Finset.indicator_biUnion_apply | Mathlib.Algebra.BigOperators.Group.Finset.Indicator | ∀ {ι : Type u_1} {κ : Type u_2} {β : Type u_4} [inst : AddCommMonoid β] (s : Finset ι) (t : ι → Set κ) {f : κ → β},
(↑s).PairwiseDisjoint t → ∀ (x : κ), (⋃ i ∈ s, t i).indicator f x = ∑ i ∈ s, (t i).indicator f x | null | true |
CentroidHom.copy | Mathlib.Algebra.Ring.CentroidHom | {α : Type u_5} → [inst : NonUnitalNonAssocSemiring α] → (f : CentroidHom α) → (f' : α → α) → f' = ⇑f → CentroidHom α | Copy of a `CentroidHom` with a new `toFun` equal to the old one. Useful to fix
definitional equalities. | true |
_private.Init.Data.Array.Erase.0.Array.set_eraseIdx_le._proof_1 | Init.Data.Array.Erase | ∀ {α : Type u_1} {xs : Array α} {i : ℕ} {w : i < xs.size} {j : ℕ}, j < xs.size - 1 → ¬j + 1 < xs.size → False | null | false |
Lean.PrettyPrinter.Parenthesizer.checkLineEq.parenthesizer | Lean.PrettyPrinter.Parenthesizer | Lean.PrettyPrinter.Parenthesizer | null | true |
Polynomial.IsSplittingField.rec | Mathlib.FieldTheory.SplittingField.IsSplittingField | {K : Type v} →
{L : Type w} →
[inst : Field K] →
[inst_1 : Field L] →
[inst_2 : Algebra K L] →
{f : Polynomial K} →
{motive : Polynomial.IsSplittingField K L f → Sort u} →
((splits' : (Polynomial.map (algebraMap K L) f).Splits) →
(adjoin_rootSet'... | null | false |
MeasureTheory.L1.integralCLM'.congr_simp | Mathlib.MeasureTheory.Integral.Bochner.L1 | ∀ {α : Type u_1} {E : Type u_2} (𝕜 : Type u_4) [inst : NormedAddCommGroup E] {m : MeasurableSpace α}
{μ : MeasureTheory.Measure α} [inst_1 : NormedSpace ℝ E] [inst_2 : NormedRing 𝕜] [inst_3 : Module 𝕜 E]
[inst_4 : IsBoundedSMul 𝕜 E] [inst_5 : SMulCommClass ℝ 𝕜 E] [inst_6 : CompleteSpace E],
MeasureTheory.L1.... | null | true |
Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero._proof_1 | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | ∀ {R : Type u_1} [inst : Field R] (a b : R), a ≠ 0 → !![a, b; 0, a⁻¹].det = 1 | null | false |
_private.Mathlib.MeasureTheory.Measure.Support.0.MeasureTheory.Measure.support_eq_forall_isOpen._simp_1_1 | Mathlib.MeasureTheory.Measure.Support | ∀ {α : Type u} {a b : Set α}, (a = b) = ∀ (x : α), x ∈ a ↔ x ∈ b | null | false |
PadicInt.subring._proof_3 | Mathlib.NumberTheory.Padics.PadicIntegers | ∀ (p : ℕ) [hp : Fact (Nat.Prime p)] {a b : ℚ_[p]}, a ∈ {x | ‖x‖ ≤ 1} → b ∈ {x | ‖x‖ ≤ 1} → ‖a * b‖ ≤ 1 | null | false |
normalizedGCDMonoidOfExistsLCM._proof_2 | Mathlib.Algebra.GCDMonoid.Basic | ∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α]
(h : ∀ (a b : α), ∃ c, ∀ (d : α), a ∣ d ∧ b ∣ d ↔ c ∣ d) (a b : α), b ∣ normalize (Classical.choose ⋯) | null | false |
CategoryTheory.Over.mapFunctor_obj | Mathlib.CategoryTheory.Comma.Over.Basic | ∀ (T : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} T] (X : T),
(CategoryTheory.Over.mapFunctor T).obj X = CategoryTheory.Cat.of (CategoryTheory.Over X) | null | true |
Lean.Option._sizeOf_inst | Lean.Data.Options | (α : Type) → [SizeOf α] → SizeOf (Lean.Option α) | null | false |
Ordinal.veblen_eq_of_lt_invVeblen₁ | Mathlib.SetTheory.Ordinal.Veblen | ∀ {o x : Ordinal.{u}}, o < x.invVeblen₁ → Ordinal.veblen o x = x | null | true |
_private.Mathlib.Data.List.Basic.0.List.mem_dropLast_of_mem_of_ne_getLast._proof_1_5 | Mathlib.Data.List.Basic | ∀ {α : Type u_1} {l : List α} {a : α} (ha : a ∈ l), ¬l.dropLast ++ [l.getLast ⋯] = [] | null | false |
MeasureTheory.Measure.haarScalarFactor.eq_1 | Mathlib.MeasureTheory.Measure.Haar.Unique | ∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
[inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] (μ' μ : MeasureTheory.Measure G) [inst_5 : μ.IsHaarMeasure]
[inst_6 : MeasureTheory.IsFiniteMeasureOnCompacts μ'] [inst_7 : μ'.IsMulLeftInvariant],
μ'.haarScalarFact... | null | true |
_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.TextbasedLinter | Mathlib.Tactic.Linter.TextBased | Type | Core logic of a text based linter: given a collection of lines,
return an array of all style errors with (1-based!) line numbers. If possible,
also return the collection of all lines, changed as needed to fix the linter errors.
(Such automatic fixes are only possible for some kinds of `StyleError`s.)
| true |
_private.Mathlib.Data.Set.Inclusion.0.Set.eq_of_inclusion_surjective._proof_1_2 | Mathlib.Data.Set.Inclusion | ∀ {α : Type u_1} {s t : Set α} {h : s ⊆ t}, Function.Surjective (Set.inclusion h) → ∀ x ∈ t, x ∈ s | null | false |
ISize.pow_succ | Init.Data.SInt.Lemmas | ∀ (x : ISize) (n : ℕ), x ^ (n + 1) = x ^ n * x | null | true |
HasDerivAt.fun_add | Mathlib.Analysis.Calculus.Deriv.Add | ∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜},
HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (fun i => f i + g i) (f' + g') x | Eta-expanded form of `HasDerivAt.add` | true |
mul_le_mul_right' | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | ∀ {α : Type u_1} [inst : Mul α] [inst_1 : LE α] [i : MulRightMono α] {b c : α}, b ≤ c → ∀ (a : α), b * a ≤ c * a | **Alias** of `mul_le_mul_left`. | true |
Matrix.SpecialLinearGroup.mapGL_inj | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs | ∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {S : Type u_1}
[inst_3 : CommRing S] [inst_4 : Algebra R S] [FaithfulSMul R S] (g g' : Matrix.SpecialLinearGroup n R),
(Matrix.SpecialLinearGroup.mapGL S) g = (Matrix.SpecialLinearGroup.mapGL S) g' ↔ g = g' | null | true |
MonoidAlgebra.mapDomainBialgHom | Mathlib.RingTheory.Bialgebra.MonoidAlgebra | (R : Type u_1) →
{M : Type u_3} →
{N : Type u_4} →
[inst : CommSemiring R] →
[inst_1 : Monoid M] → [inst_2 : Monoid N] → (M →* N) → MonoidAlgebra R M →ₐc[R] MonoidAlgebra R N | If `f : M → N` is a monoid hom, then `MonoidAlgebra.mapDomain f` is a bialgebra hom between
their monoid algebras. | true |
Std.Tactic.BVDecide.LRAT.Internal.unsat_of_cons_none_unsat | Std.Tactic.BVDecide.LRAT.Internal.Convert | ∀ {n : ℕ} (clauses : List (Option (Std.Tactic.BVDecide.LRAT.Internal.DefaultClause n))),
Std.Tactic.BVDecide.LRAT.Internal.Unsatisfiable (Std.Tactic.BVDecide.LRAT.Internal.PosFin n)
(Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ofArray (none :: clauses).toArray) →
Std.Tactic.BVDecide.LRAT.Internal.Unsat... | null | true |
PiTensorProduct.mapL_apply | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | ∀ {ι : Type uι} [inst : Fintype ι] {𝕜 : Type u𝕜} [inst_1 : NontriviallyNormedField 𝕜] {E : ι → Type uE}
[inst_2 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)] {E' : ι → Type u_1}
[inst_4 : (i : ι) → SeminormedAddCommGroup (E' i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (E' i)]
(... | null | true |
LocallyConstant.instAddMonoidWithOne._proof_4 | Mathlib.Topology.LocallyConstant.Algebra | ∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : AddMonoidWithOne Y] (x : ℕ)
(x_1 : LocallyConstant X Y), ⇑(x • x_1) = ⇑(x • x_1) | null | false |
_private.Mathlib.Topology.Inseparable.0.inseparable_iff_forall_isClosed._simp_1_4 | Mathlib.Topology.Inseparable | ∀ {a b : Prop}, ((a → b) ∧ (b → a)) = (a ↔ b) | null | false |
Nat.stirlingSecond.eq_4 | Mathlib.Combinatorics.Enumerative.Stirling | ∀ (n k : ℕ), n.succ.stirlingSecond k.succ = (k + 1) * n.stirlingSecond (k + 1) + n.stirlingSecond k | null | true |
precMin1 | Init.Notation | Lean.ParserDescr | `(min+1)` (we can only write `min+1` after `Meta.lean`) | true |
Homeomorph.toMeasurableEquiv.congr_simp | Mathlib.MeasureTheory.Function.LocallyIntegrable | ∀ {γ : Type u_3} {γ₂ : Type u_4} [inst : TopologicalSpace γ] [inst_1 : MeasurableSpace γ] [inst_2 : BorelSpace γ]
[inst_3 : TopologicalSpace γ₂] [inst_4 : MeasurableSpace γ₂] [inst_5 : BorelSpace γ₂] (h h_1 : γ ≃ₜ γ₂),
h = h_1 → h.toMeasurableEquiv = h_1.toMeasurableEquiv | null | true |
Circle.instMetricSpace._proof_5 | Mathlib.Analysis.Complex.Circle | ∀ (x y z : Circle), dist x z ≤ dist x y + dist y z | null | false |
Set.mem_list_prod | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | ∀ {α : Type u_1} [inst : Monoid α] {l : List (Set α)} {a : α},
a ∈ l.prod ↔ ∃ l', (List.map (fun x => ↑x.snd) l').prod = a ∧ List.map Sigma.fst l' = l | null | true |
FiberBundle.extend_apply_self | Mathlib.Topology.FiberBundle.Basic | ∀ {B : Type u_2} (F : Type u_3) {E : B → Type u_5} [inst : TopologicalSpace B] [inst_1 : TopologicalSpace F]
[inst_2 : (x : B) → TopologicalSpace (E x)] [inst_3 : (x : B) → Zero (E x)]
[inst_4 : TopologicalSpace (Bundle.TotalSpace F E)] [inst_5 : FiberBundle F E] {x : B} (v : E x),
FiberBundle.extend F v x = v | null | true |
MvPolynomial.coeffAddMonoidHom_apply | Mathlib.Algebra.MvPolynomial.Basic | ∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (m : σ →₀ ℕ) (p : MvPolynomial σ R),
(MvPolynomial.coeffAddMonoidHom m) p = MvPolynomial.coeff m p | null | true |
PartialEquiv.refl_source | Mathlib.Logic.Equiv.PartialEquiv | ∀ {α : Type u_1}, (PartialEquiv.refl α).source = Set.univ | null | true |
Concept.instInfSet._proof_1 | Mathlib.Order.Concept | ∀ {α : Type u_1} {β : Type u_2} {r : α → β → Prop} (S : Set (Concept α β r)), Order.IsExtent r (⋂ i ∈ S, i.extent) | null | false |
_private.Init.Data.List.ToArray.0.List.mapA.match_1.eq_2 | Init.Data.List.ToArray | ∀ {α : Type u_1} (motive : List α → Sort u_2) (a : α) (as : List α) (h_1 : Unit → motive [])
(h_2 : (a : α) → (as : List α) → motive (a :: as)),
(match a :: as with
| [] => h_1 ()
| a :: as => h_2 a as) =
h_2 a as | null | true |
Algebra.Presentation.ofAlgEquiv_toGenerators | Mathlib.RingTheory.Extension.Presentation.Basic | ∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Presentation R S ι σ) {T : Type u_1} [inst_3 : CommRing T] [inst_4 : Algebra R T] (e : S ≃ₐ[R] T),
(P.ofAlgEquiv e).toGenerators = P.ofAlgEquiv e | null | true |
PrimeSpectrum.closedsEmbedding | Mathlib.RingTheory.Spectrum.Prime.Topology | (R : Type u_1) → [inst : CommSemiring R] → (TopologicalSpace.Closeds (PrimeSpectrum R))ᵒᵈ ↪o Ideal R | The antitone order embedding of closed subsets of `Spec R` into ideals of `R`. | true |
Int16.ofInt_bitVecToInt | Init.Data.SInt.Lemmas | ∀ (n : BitVec 16), Int16.ofInt n.toInt = Int16.ofBitVec n | null | true |
Std.ExtHashMap.mem_of_mem_insertIfNew' | Std.Data.ExtHashMap.Lemmas | ∀ {α : Type u} {β : Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.ExtHashMap α β} [inst : EquivBEq α]
[inst_1 : LawfulHashable α] {k a : α} {v : β}, a ∈ m.insertIfNew k v → ¬((k == a) = true ∧ k ∉ m) → a ∈ m | This is a restatement of `mem_of_mem_insertIfNew` that is written to exactly match the proof obligation
in the statement of `getElem_insertIfNew`. | true |
DivInvOneMonoid.rec | Mathlib.Algebra.Group.Defs | {G : Type u_2} →
{motive : DivInvOneMonoid G → Sort u} →
([toDivInvMonoid : DivInvMonoid G] →
(inv_one : 1⁻¹ = 1) → motive { toDivInvMonoid := toDivInvMonoid, inv_one := inv_one }) →
(t : DivInvOneMonoid G) → motive t | null | false |
Sum.Lex.inlLatticeHom._proof_2 | Mathlib.Data.Sum.Lattice | ∀ {α : Type u_1} {β : Type u_2} [inst : Lattice α] (x x_1 : α), Sum.inlₗ (x ⊓ x_1) = Sum.inlₗ (x ⊓ x_1) | null | false |
CategoryTheory.GrothendieckTopology.instInhabited | Mathlib.CategoryTheory.Sites.Grothendieck | {C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → Inhabited (CategoryTheory.GrothendieckTopology C) | null | true |
OpenPartialHomeomorph.coe_toPartialEquiv_symm | Mathlib.Topology.OpenPartialHomeomorph.Defs | ∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y), ↑e.symm = ↑e.symm | null | true |
MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts | Mathlib.MeasureTheory.Measure.Regular | ∀ {α : Type u_1} {inst : MeasurableSpace α} {inst_1 : TopologicalSpace α} {μ : MeasureTheory.Measure α}
[self : μ.Regular], MeasureTheory.IsFiniteMeasureOnCompacts μ | null | true |
_private.Mathlib.Tactic.Attr.Register.0.initFn._@.Mathlib.Tactic.Attr.Register.1988518680._hygCtx._hyg.5 | Mathlib.Tactic.Attr.Register | IO Lean.Meta.SimpExtension | null | false |
String.Slice.Pattern.Model.IsValidRevSearchFrom.matched_of_eq | Init.Data.String.Lemmas.Pattern.Basic | ∀ {ρ : Type} {pat : ρ} [inst : String.Slice.Pattern.Model.PatternModel pat] {s : String.Slice}
{startPos endPos endPos' : s.Pos} {l : List (String.Slice.Pattern.SearchStep s)},
String.Slice.Pattern.Model.IsValidRevSearchFrom pat startPos l →
String.Slice.Pattern.Model.IsLongestRevMatchAt pat startPos endPos' →
... | null | true |
Lean.Elab.UserWidgetInfo.mk.inj | Lean.Elab.InfoTree.Types | ∀ {toWidgetInstance : Lean.Widget.WidgetInstance} {stx : Lean.Syntax} {toWidgetInstance_1 : Lean.Widget.WidgetInstance}
{stx_1 : Lean.Syntax},
{ toWidgetInstance := toWidgetInstance, stx := stx } = { toWidgetInstance := toWidgetInstance_1, stx := stx_1 } →
toWidgetInstance = toWidgetInstance_1 ∧ stx = stx_1 | null | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.