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.Homology.DerivedCategory.TStructure.0.DerivedCategory.isGE_Q_obj_iff._simp_1_2 | Mathlib.Algebra.Homology.DerivedCategory.TStructure | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(K : CochainComplex C ℤ) (n : ℤ), K.IsGE n = ∀ i < n, HomologicalComplex.ExactAt K i | null | false |
PresheafOfModules.homMk._proof_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
{M₁ M₂ : PresheafOfModules R} (φ : M₁.presheaf ⟶ M₂.presheaf) (X : Cᵒᵖ) (x y : ↑(M₁.1 X)),
(CategoryTheory.ConcreteCategory.hom (φ.app X)) (x + y) =
(CategoryTheory.ConcreteCategory.hom (φ.app X)) x + (Catego... | null | false |
WType.brecOn | Mathlib.Data.W.Basic | {α : Type u_1} →
{β : α → Type u_2} →
{motive : WType β → Sort u} → (t : WType β) → ((t : WType β) → WType.below t → motive t) → motive t | null | false |
SimpleGraph.center_top | Mathlib.Combinatorics.SimpleGraph.Diam | ∀ {α : Type u_1}, ⊤.center = Set.univ | null | true |
Char.any | Batteries.Data.Char.Basic | (Char → Bool) → Bool | Returns `true` if `p` returns true for some `Char`. | true |
CategoryTheory.RetractArrow.map_i_left | Mathlib.CategoryTheory.Retract | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
{X Y Z W : C} {f : X ⟶ Y} {g : Z ⟶ W} (h : CategoryTheory.RetractArrow f g) (F : CategoryTheory.Functor C D),
(h.map F).i.left = F.map (CategoryTheory.Arrow.Hom.left h.i) | null | true |
IsScalarTower.of_compHom | Mathlib.Algebra.Algebra.Tower | ∀ (R : Type u) (A : Type w) (M : Type v₁) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : MulAction A M], IsScalarTower R A M | null | true |
ContDiffMapSupportedIn.integralAgainstBilinLM_eq_integral | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | ∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace ℝ E] {n : ℕ∞} {K : TopologicalSpace.Compacts E} {m : MeasurableSpace E}
[inst_3 : OpensMeasurableSpace E] {F₁ : Type u_5} {F₂ : Type u_6} {F₃ : Type u_7} [inst_4 : NormedAddCommGroup F₁]
[ins... | null | true |
OrthonormalBasis.repr_injective | Mathlib.Analysis.InnerProductSpace.PiL2 | ∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι], Function.Injective OrthonormalBasis.repr | null | true |
_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ._simp_1_2 | Mathlib.Data.Int.Interval | ∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a b : α}, (a ∈ insert b s) = (a = b ∨ a ∈ s) | null | false |
ShiftRight.recOn | Init.Prelude | {α : Type u} →
{motive : ShiftRight α → Sort u_1} →
(t : ShiftRight α) → ((shiftRight : α → α → α) → motive { shiftRight := shiftRight }) → motive t | null | false |
Finset.filter_subset._simp_1 | Mathlib.Data.Finset.Filter | ∀ {α : Type u_1} (p : α → Prop) [inst : DecidablePred p] (s : Finset α), (Finset.filter p s ⊆ s) = True | null | false |
Matrix.transpose_hadamard | Mathlib.LinearAlgebra.Matrix.Hadamard | ∀ {α : Type u_1} {m : Type u_2} {n : Type u_3} [inst : Mul α] (A B : Matrix m n α),
(A.hadamard B).transpose = A.transpose.hadamard B.transpose | null | true |
CategoryTheory.ModObj.rec | Mathlib.CategoryTheory.Monoidal.Mod | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.MonoidalCategory C] →
{D : Type u₂} →
[inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
[inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] →
{M : C} →
[inst_4 : Cat... | null | false |
RingHom.closure_preimage_le | Mathlib.Algebra.Ring.Subring.Basic | ∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (f : R →+* S) (s : Set S),
Subring.closure (⇑f ⁻¹' s) ≤ Subring.comap f (Subring.closure s) | null | true |
Finset.add_subset_add_left | Mathlib.Algebra.Group.Pointwise.Finset.Basic | ∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Add α] {s t₁ t₂ : Finset α}, t₁ ⊆ t₂ → s + t₁ ⊆ s + t₂ | null | true |
SheafOfModules.hom_ext_iff | Mathlib.Algebra.Category.ModuleCat.Sheaf | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
{R : CategoryTheory.Sheaf J RingCat} {X Y : SheafOfModules R} {f g : X ⟶ Y}, f = g ↔ f.val = g.val | null | true |
Turing.TM1.stmts | Mathlib.Computability.TuringMachine.PostTuringMachine | {Γ : Type u_1} →
{Λ : Type u_2} → {σ : Type u_3} → (Λ → Turing.TM1.Stmt Γ Λ σ) → Finset Λ → Finset (Option (Turing.TM1.Stmt Γ Λ σ)) | The set of all statements in a Turing machine, plus one extra value `none` representing the
halt state. This is used in the TM1 to TM0 reduction. | true |
DiscreteUniformity.mk._flat_ctor | Mathlib.Topology.UniformSpace.DiscreteUniformity | ∀ {X : Type u_1} [u : UniformSpace X], u = ⊥ → DiscreteUniformity X | null | false |
FinPartOrd.dualEquiv_unitIso | Mathlib.Order.Category.FinPartOrd | FinPartOrd.dualEquiv.unitIso =
CategoryTheory.NatIso.ofComponents (fun X => FinPartOrd.Iso.mk (OrderIso.dualDual ↑X.toPartOrd))
@FinPartOrd.dualEquiv._proof_1 | null | true |
algebraMap_smul | Mathlib.Algebra.Algebra.Basic | ∀ {R : Type u_1} [inst : CommSemiring R] (A : Type u_2) [inst_1 : Semiring A] [inst_2 : Algebra R A] {M : Type u_3}
[inst_3 : AddCommMonoid M] [inst_4 : Module A M] [inst_5 : Module R M] [IsScalarTower R A M] (r : R) (m : M),
(algebraMap R A) r • m = r • m | null | true |
DifferentiableOn.inverse | Mathlib.Analysis.Calculus.FDeriv.Mul | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {R : Type u_5} [inst_3 : NormedRing R] [HasSummableGeomSeries R]
[inst_5 : NormedAlgebra 𝕜 R] {h : E → R} {S : Set E},
DifferentiableOn 𝕜 h S → (∀ x ∈ S, IsUnit (h x)) → Differentiabl... | null | true |
SymAlg.instNonAssocRingOfInvertibleOfNat._proof_14 | Mathlib.Algebra.Symmetrized | ∀ {α : Type u_1} [inst : Ring α] [inst_1 : Invertible 2] (a : αˢʸᵐ), a * 1 = a | null | false |
pi_generateFrom_eq_finite | Mathlib.Topology.Constructions | ∀ {ι : Type u_5} {X : ι → Type u_9} {g : (a : ι) → Set (Set (X a))} [Finite ι],
(∀ (a : ι), ⋃₀ g a = Set.univ) →
Pi.topologicalSpace = TopologicalSpace.generateFrom {t | ∃ s, (∀ (a : ι), s a ∈ g a) ∧ t = Set.univ.pi s} | null | true |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper.0.AlgebraicGeometry.Proj.valuativeCriterion_existence_aux._simp_1_11 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | ∀ (A : Type u) [inst : CommRing A] (K : Type v) [inst_1 : Field K] [inst_2 : Algebra A K] [inst_3 : IsDomain A]
[inst_4 : ValuationRing A] [inst_5 : IsFractionRing A K] (x : K),
(x ∈ (ValuationRing.valuation A K).integer) = ∃ a, (algebraMap A K) a = x | null | false |
TwoSidedIdeal.asIdealOpposite | Mathlib.RingTheory.TwoSidedIdeal.Operations | {R : Type u_1} → [inst : Ring R] → TwoSidedIdeal R →o Ideal Rᵐᵒᵖ | Every two-sided ideal is also a right ideal. | true |
Mathlib.Meta.NormNum.evalIsSquareRat | Mathlib.Tactic.NormNum.IsSquare | Mathlib.Meta.NormNum.NormNumExt | `norm_num` extension for `IsSquare` on `ℚ`. | true |
BddOrd.mk.injEq | Mathlib.Order.Category.BddOrd | ∀ (toPartOrd : PartOrd) [isBoundedOrder : BoundedOrder ↑toPartOrd] (toPartOrd_1 : PartOrd)
(isBoundedOrder_1 : BoundedOrder ↑toPartOrd_1),
({ toPartOrd := toPartOrd, isBoundedOrder := isBoundedOrder } =
{ toPartOrd := toPartOrd_1, isBoundedOrder := isBoundedOrder_1 }) =
(toPartOrd = toPartOrd_1 ∧ isBounde... | null | true |
Std.MaxEqOr | Init.Data.Order.Classes | (α : Type u) → [Max α] → Prop | This typeclass states that `Max.max a b` returns one of its arguments, either `a` or `b`.
| true |
BitVec.ofInt_iSizeToInt | Init.Data.SInt.Lemmas | ∀ (x : ISize), BitVec.ofInt System.Platform.numBits x.toInt = x.toBitVec | null | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.exists_linearIndepOn_extension.match_1_1 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | ∀ {ι : Type u_2} {V : Type u_1} {v : ι → V} {t : Set ι} (x : V) (motive : x ∈ v '' t → Prop) (x_1 : x ∈ v '' t),
(∀ (x_2 : ι) (hx : x_2 ∈ t) (hvx : v x_2 = x), motive ⋯) → motive x_1 | null | false |
Btw.rec | Mathlib.Order.Circular | {α : Type u_1} → {motive : Btw α → Sort u} → ((btw : α → α → α → Prop) → motive { btw := btw }) → (t : Btw α) → motive t | null | false |
AddAut.vadd_def | Mathlib.Algebra.Group.Action.End | ∀ {M : Type u_2} [inst : AddMonoid M] (f : AddAut M) (a : M), f +ᵥ a = f a | null | true |
Metric.nonneg_of_mem_closedBall | Mathlib.Topology.MetricSpace.Pseudo.Defs | ∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε : ℝ}, y ∈ Metric.closedBall x ε → 0 ≤ ε | null | true |
MeasurableSpace.DynkinSystem.instPartialOrder._proof_3 | Mathlib.MeasureTheory.PiSystem | ∀ {α : Type u_1} (x x_1 x_2 : MeasurableSpace.DynkinSystem α), x ≤ x_1 → x_1 ≤ x_2 → x ≤ x_2 | null | false |
Std.DTreeMap.Internal.Impl.getKey._sunfold | Std.Data.DTreeMap.Internal.Queries | {α : Type u} →
{β : α → Type v} →
[inst : Ord α] → (t : Std.DTreeMap.Internal.Impl α β) → (k : α) → Std.DTreeMap.Internal.Impl.contains k t = true → α | null | false |
LinearMap.addMonoid._proof_3 | Mathlib.Algebra.Module.LinearMap.Defs | ∀ {R₁ : Type u_1} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : Semiring R₁] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R₁ M] [inst_5 : Module R₂ M₂]
{σ₁₂ : R₁ →+* R₂} (a : M →ₛₗ[σ₁₂] M₂), a + 0 = a | null | false |
BddLat.Iso.mk._proof_4 | Mathlib.Order.Category.BddLat | ∀ {α β : BddLat} (e : ↑α.toLat ≃o ↑β.toLat) (a b : ↑α.1), e (a ⊓ b) = e a ⊓ e b | null | false |
OneHom.comp_apply | Mathlib.Algebra.Group.Hom.Defs | ∀ {M : Type u_4} {N : Type u_5} {P : Type u_6} [inst : One M] [inst_1 : One N] [inst_2 : One P] (g : OneHom N P)
(f : OneHom M N) (x : M), (g.comp f) x = g (f x) | null | true |
Ideal.powQuotPowSuccLinearEquivMapMkPowSuccPow._proof_3 | Mathlib.RingTheory.Ideal.Quotient.Operations | ∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (n : ℕ), IsScalarTower R (R ⧸ I ^ (n + 1)) (R ⧸ I ^ (n + 1)) | null | false |
SimpleGraph.Copy.ext | Mathlib.Combinatorics.SimpleGraph.Copy | ∀ {α : Type u_4} {β : Type u_5} {A : SimpleGraph α} {B : SimpleGraph β} {f g : A.Copy B}, (∀ (a : α), f a = g a) → f = g | null | true |
Lean.Meta.Grind.AC.DiseqCnstrProof.erase_dup | Lean.Meta.Tactic.Grind.AC.Types | Lean.Meta.Grind.AC.DiseqCnstr → Lean.Meta.Grind.AC.DiseqCnstrProof | null | true |
BitVec.getElem?_zero_ofNat_zero | Init.Data.BitVec.Lemmas | ∀ {w : ℕ}, (0#(w + 1))[0]? = some false | null | true |
_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxi.Iterator.instIteratorLoop.loop.wf._unary._proof_2 | Init.Data.Range.Polymorphic.RangeIterator | ∀ {α : Type u_1} [inst : Std.PRange.UpwardEnumerable α] [Std.PRange.LawfulUpwardEnumerable α] (LargeEnough : α → Prop),
(∀ (a b : α), Std.PRange.UpwardEnumerable.LE a b → LargeEnough a → LargeEnough b) →
∀ (next : α), LargeEnough next → ∀ (next' : α), Std.PRange.succ? next = some next' → LargeEnough next' | null | false |
Filter.pureAddHom._proof_1 | Mathlib.Order.Filter.Pointwise | ∀ {α : Type u_1} [inst : Add α] (x x_1 : α), pure (x + x_1) = pure x + pure x_1 | null | false |
FreeMonoid.lift.eq_1 | Mathlib.Algebra.FreeMonoid.Basic | ∀ {α : Type u_1} {M : Type u_4} [inst : Monoid M],
FreeMonoid.lift =
{
toFun := fun f =>
{ toFun := fun l => FreeMonoid.prodAux (List.map f (FreeMonoid.toList l)), map_one' := ⋯, map_mul' := ⋯ },
invFun := fun f x => f (FreeMonoid.of x), left_inv := ⋯, right_inv := ⋯ } | null | true |
Sum.swap_swap_eq | Init.Data.Sum.Lemmas | ∀ {α : Type u_1} {β : Type u_2}, Sum.swap ∘ Sum.swap = id | null | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_382 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | Lean.Syntax | null | false |
UniformSpace.hausdorff | Mathlib.Topology.UniformSpace.Closeds | (α : Type u_1) → [UniformSpace α] → UniformSpace (Set α) | The Hausdorff uniformity on the powerset of a uniform space. Used for defining the uniformities
on `Closeds`, `Compacts` and `NonemptyCompacts`.
See note [reducible non-instances]. | true |
CovariantDerivative.difference | Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Basic | {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} →
... | The difference of two covariant derivatives, as a one-form taking values in the
endomorphisms of `V`. | true |
CategoryTheory.MorphismProperty.HasPushoutsAgainst.casesOn | Mathlib.CategoryTheory.MorphismProperty.Limits | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{P P' : CategoryTheory.MorphismProperty C} →
{motive : P.HasPushoutsAgainst P' → Sort u_1} →
(t : P.HasPushoutsAgainst P') →
((hasPushoutsAlong : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), P' f → P.HasPushoutsAlong f) → motive ⋯) → motive t | null | false |
Sum.getRight_eq_getRight? | Mathlib.Data.Sum.Basic | ∀ {α : Type u} {β : Type v} {x : α ⊕ β} (h₁ : x.isRight = true) (h₂ : x.getRight?.isSome = true),
x.getRight h₁ = x.getRight?.get h₂ | null | true |
Lean.Meta.Sym.getInt16Value? | Lean.Meta.Sym.LitValues | Lean.Expr → OptionT Id Int16 | null | true |
VectorPrebundle.totalSpaceTopology | Mathlib.Topology.VectorBundle.Basic | {R : Type u_1} →
{B : Type u_2} →
{F : Type u_3} →
{E : B → Type u_4} →
[inst : NontriviallyNormedField R] →
[inst_1 : (x : B) → AddCommMonoid (E x)] →
[inst_2 : (x : B) → Module R (E x)] →
[inst_3 : NormedAddCommGroup F] →
[inst_4 : NormedSpace R ... | Topology on the total space that will make the prebundle into a bundle. | true |
Submodule.instDiv._proof_1 | Mathlib.Algebra.Algebra.Operations | ∀ {R : Type u_2} [inst : CommSemiring R] {A : Type u_1} [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
(I J : Submodule R A) {a b : A},
a ∈ {x | ∀ y ∈ J, x * y ∈ I} → b ∈ {x | ∀ y ∈ J, x * y ∈ I} → ∀ y ∈ J, (a + b) * y ∈ I | null | false |
PowerSeries.HasSubst | Mathlib.RingTheory.PowerSeries.Substitution | {τ : Type u_3} → {S : Type u_4} → [CommRing S] → MvPowerSeries τ S → Prop | (Possibly multivariate) power series which can be substituted in a `PowerSeries`. | true |
SeminormedCommGroup | Mathlib.Analysis.Normed.Group.Defs | Type u_8 → Type u_8 | A seminormed group is a group endowed with a norm for which `dist x y = ‖x⁻¹ * y‖`
defines a pseudometric space structure. | true |
_private.Lean.Elab.Tactic.Grind.Config.0.Lean.Elab.Tactic.instEvalExprConfig | Lean.Elab.Tactic.Grind.Config | Lean.Elab.ConfigEval.EvalExpr Lean.Grind.Config | null | true |
Topology.IsQuotientMap.trivializationOfVAddDisjoint._proof_8 | Mathlib.Topology.Covering.Quotient | ∀ {E : Type u_2} {X : Type u_1} {f : E → X} {G : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G E] (U : Set E),
(∀ (g : G) (e : E), f (g +ᵥ e) = f e) → ∀ (g : G) ⦃x : X⦄, x ∈ f '' U → x ∈ f '' (fun x => g +ᵥ x) ⁻¹' U | null | false |
Computability.«term_≡ᵀ_» | Mathlib.Computability.TuringDegree | Lean.TrailingParserDescr | `f` is Turing equivalent to `g` if `f` is reducible to `g` and `g` is reducible to `f`.
| true |
Vector.push_inj_left | Init.Data.Vector.Lemmas | ∀ {α : Type u_1} {n : ℕ} {a : α} {xs ys : Vector α n}, xs.push a = ys.push a ↔ xs = ys | null | true |
Lean.mkPtrSet | Lean.Util.PtrSet | {α : Type} → optParam ℕ 64 → Lean.PtrSet α | null | true |
LinearMap.FiniteRangeSetoid.setoid | Mathlib.Algebra.Module.LinearMap.FiniteRange | {K : Type u_1} →
{V : Type u_2} →
{V₂ : Type u_4} →
[inst : CommRing K] →
[inst_1 : AddCommGroup V] →
[inst_2 : Module K V] → [inst_3 : AddCommGroup V₂] → [inst_4 : Module K V₂] → Setoid (V →ₗ[K] V₂) | This is the equivalence relation on linear maps such that `u ≈ v` precisely
when `u - v` is a linear map with noetherian range. We allow ourself this slightly abusive name
because the more natural definition (`u - v` has finitely generated range) only yields a
well-behaved relation (more precisely, an additive congruen... | true |
WittVector.nsmul_coeff | Mathlib.RingTheory.WittVector.Defs | ∀ {p : ℕ} {R : Type u_1} [hp : Fact (Nat.Prime p)] [inst : CommRing R] (m : ℕ) (x : WittVector p R) (n : ℕ),
(m • x).coeff n = WittVector.peval (WittVector.wittNSMul p m n) ![x.coeff] | null | true |
MeasureTheory.instMetrizableSpaceProbabilityMeasure | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | ∀ (X : Type u_2) [inst : TopologicalSpace X] [TopologicalSpace.PseudoMetrizableSpace X]
[TopologicalSpace.SeparableSpace X] [inst_3 : MeasurableSpace X] [inst_4 : BorelSpace X],
TopologicalSpace.MetrizableSpace (MeasureTheory.ProbabilityMeasure X) | The topology of convergence in distribution on a separable Borel space is metrizable. | true |
Subgroup.IsSubnormal.recOn | Mathlib.GroupTheory.IsSubnormal | ∀ {G : Type u_1} [inst : Group G] {motive : (a : Subgroup G) → a.IsSubnormal → Prop} {a : Subgroup G}
(t : a.IsSubnormal),
motive ⊤ ⋯ →
(∀ (H K : Subgroup G) (h_le : H ≤ K) (hSubn : K.IsSubnormal) (hN : (H.subgroupOf K).Normal),
motive K hSubn → motive H ⋯) →
motive a t | null | false |
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom._default | Mathlib.CategoryTheory.Monoidal.Action.Basic | {C : Type u_1} →
{D : Type u_2} →
{inst : CategoryTheory.Category.{v_1, u_1} C} →
{inst_1 : CategoryTheory.Category.{v_2, u_2} D} →
{inst_2 : CategoryTheory.MonoidalCategoryStruct C} →
(actionObj : C → D → D) →
({c c' : C} → (c ⟶ c') → (d : D) → actionObj c d ⟶ actionObj c' d) ... | null | false |
Subtype.forall_set_subtype | Mathlib.Data.Set.Image | ∀ {α : Type u_1} {t : Set α} (p : Set α → Prop), (∀ (s : Set ↑t), p (Subtype.val '' s)) ↔ ∀ s ⊆ t, p s | null | true |
Lean.Lsp.instFileSourceSignatureHelpParams | Lean.Server.FileSource | Lean.Lsp.FileSource Lean.Lsp.SignatureHelpParams | null | true |
_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat | Mathlib.Computability.TuringDegree | Preorder (ℕ →. ℕ) | null | true |
SimpleGraph.Subgraph.botIso._proof_2 | Mathlib.Combinatorics.SimpleGraph.Subgraph | ∀ {V : Type u_1} {G : SimpleGraph V} (x : ↑⊥.verts), (False.elim ⋯).elim = x | null | false |
CategoryTheory.Grothendieck.map._proof_2 | Mathlib.CategoryTheory.Grothendieck | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {F G : CategoryTheory.Functor C CategoryTheory.Cat}
(α : F ⟶ G) (X : CategoryTheory.Grothendieck F),
{ base := (CategoryTheory.CategoryStruct.id X).base,
fiber :=
CategoryTheory.CategoryStruct.comp ((CategoryTheory.eqToHom ⋯).toNatTrans.ap... | null | false |
Option.filter_some | Init.Data.Option.Lemmas | ∀ {α : Type u_1} {p : α → Bool} {a : α}, Option.filter p (some a) = if p a = true then some a else none | null | true |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper.0.AlgebraicGeometry.Proj.isSeparated._simp_5 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | ∀ {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map g) (AlgebraicGeometry.Spec.map f) =
AlgebraicGeometry.Spec.map (CategoryTheory.CategoryStruct.comp f g) | null | false |
String.Slice.contains_char_eq_contains_beq | Init.Data.String.Lemmas.Pattern.Char | ∀ {c : Char} {s : String.Slice}, s.contains c = s.contains fun x => x == c | null | true |
MvPowerSeries.instInv | Mathlib.RingTheory.MvPowerSeries.Inverse | {σ : Type u_1} → {k : Type u_3} → [Field k] → Inv (MvPowerSeries σ k) | null | true |
CategoryTheory.SimplicialObject.Splitting.IndexSet.id | Mathlib.AlgebraicTopology.SimplicialObject.Split | (Δ : SimplexCategoryᵒᵖ) → CategoryTheory.SimplicialObject.Splitting.IndexSet Δ | The distinguished element in `Splitting.IndexSet Δ` which corresponds to the
identity of `Δ`. | true |
Lean.Elab.Tactic.closeMainGoal | Lean.Elab.Tactic.Basic | Lean.Name → Lean.Expr → optParam Bool true → Lean.Elab.Tactic.TacticM Unit | Closes main goal using the given expression.
If `checkUnassigned == true`, then `val` must not contain unassigned metavariables.
Returns `true` if `val` was successfully used to close the goal.
| true |
Turing.TM1to0.trAux._sunfold | Mathlib.Computability.TuringMachine.PostTuringMachine | {Γ : Type u_1} →
{Λ : Type u_2} →
{σ : Type u_3} →
(M : Λ → Turing.TM1.Stmt Γ Λ σ) → Γ → Turing.TM1.Stmt Γ Λ σ → σ → Turing.TM1to0.Λ' M × Turing.TM0.Stmt Γ | null | false |
Lean.Elab.GoalsAtResult | Lean.Server.InfoUtils | Type | null | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_2 | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | ∀ {α : Type u} {P : List α → Prop}, (∃ l, P l) = ∃ n f, P (List.ofFn f) | null | false |
ContinuousAlternatingMap.piLIE._proof_6 | Mathlib.Analysis.Normed.Module.Alternating.Basic | ∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {ι' : Type u_2} {F : ι' → Type u_3}
[inst_1 : (i' : ι') → SeminormedAddCommGroup (F i')] [inst_2 : (i' : ι') → NormedSpace 𝕜 (F i')],
SMulCommClass 𝕜 𝕜 ((i : ι') → F i) | null | false |
Function.IsFixedPt.eq_1 | Mathlib.Order.OmegaCompletePartialOrder | ∀ {α : Type u₁} (f : α → α) (x : α), Function.IsFixedPt f x = (f x = x) | null | true |
Dvd.noConfusion | Init.Prelude | {P : Sort u} →
{α : Type u_1} → {t : Dvd α} → {α' : Type u_1} → {t' : Dvd α'} → α = α' → t ≍ t' → Dvd.noConfusionType P t t' | null | false |
FirstOrder.Language.BoundedFormula.all_iff_not_ex_not | Mathlib.ModelTheory.Equivalence | ∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} (φ : L.BoundedFormula α (n + 1)),
T.Iff φ.all φ.not.ex.not | null | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.derivedLitsInvariant_confirmRupHint._proof_1_14 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | ∀ (rupHints : Array ℕ) (i : Fin rupHints.size), ↑i + 1 ≤ rupHints.size → ↑i < rupHints.size | null | false |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁.elim | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | {motive_7 : Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof → Sort u} →
(t : Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof) →
t.ctorIdx = 9 →
((c : Lean.Meta.Grind.Arith.Cutsat.CooperSplit) →
motive_7 (Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁ c)) →
motive_7 t | null | false |
Lean.Lsp.instToJsonChangeAnnotation.toJson | Lean.Data.Lsp.Basic | Lean.Lsp.ChangeAnnotation → Lean.Json | null | true |
Lean.Lsp.instFromJsonCallHierarchyPrepareParams.fromJson | Lean.Data.Lsp.LanguageFeatures | Lean.Json → Except String Lean.Lsp.CallHierarchyPrepareParams | null | true |
HomologicalComplex.homotopyCofiber.XIsoBiprod.congr_simp | Mathlib.Algebra.Homology.HomotopyCofiber | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_2}
{c : ComplexShape ι} {F G : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
[inst_3 : DecidableRel c.Rel] (i j : ι) (hij : c.Rel i j)
[inst_4 : CategoryTheor... | null | true |
Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueField | Mathlib.RingTheory.QuasiFinite.Weakly | ∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
(q : Ideal S) [inst_3 : q.IsPrime] [inst_4 : p.IsPrime] [q.LiesOver p] (Q : Ideal (p.Fiber S)) [inst_6 : Q.IsPrime],
Ideal.comap Algebra.TensorProduct.includeRight.toRingHom Q = q →
∀ [Algebra.QuasiFin... | Use `Algebra.QuasiFinite.of_quasiFiniteAt_residueField` instead
for `Algebra.QuasiFiniteAt R q`. | true |
Std.TreeSet.Raw.maxD_eq_iff_mem_and_forall | Std.Data.TreeSet.Raw.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet.Raw α cmp} [Std.TransCmp cmp] [Std.LawfulEqCmp cmp],
t.WF → t.isEmpty = false → ∀ {km fallback : α}, t.maxD fallback = km ↔ km ∈ t ∧ ∀ k ∈ t, (cmp k km).isLE = true | null | true |
AntitoneOn.Ico | Mathlib.Order.Interval.Set.Monotone | ∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f g : α → β} {s : Set α},
AntitoneOn f s → MonotoneOn g s → MonotoneOn (fun x => Set.Ico (f x) (g x)) s | null | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter.0.SimplexCategory.σ₀Iter_succ._proof_1_4 | Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | ∀ (i : ℕ) {n m : ℕ} (h : n + (i + 1) = m) (k : Fin ({ len := m }.len + 1)),
(CategoryTheory.ConcreteCategory.hom (SimplexCategory.σ₀Iter i ⋯)) k ≤ Fin.castSucc 0 →
(CategoryTheory.ConcreteCategory.hom (SimplexCategory.σ₀Iter i ⋯)) k ≠ Fin.last (n + 1) | null | false |
List.reduceOption_cons_of_some | Mathlib.Data.List.ReduceOption | ∀ {α : Type u_1} (x : α) (l : List (Option α)), (some x :: l).reduceOption = x :: l.reduceOption | null | true |
Ordinal.invVeblen₂_gamma | Mathlib.SetTheory.Ordinal.Veblen | ∀ (o : Ordinal.{u_1}), o.gamma.invVeblen₂ = 0 | null | true |
IsJordan.mk._flat_ctor | Mathlib.Algebra.Jordan.Basic | ∀ {A : Type u_1} [inst : Mul A],
(∀ (a b : A), a * b * a = a * (b * a)) →
(∀ (a b : A), a * a * (a * b) = a * (a * a * b)) →
(∀ (a b : A), a * a * (b * a) = a * a * b * a) →
(∀ (a b : A), a * b * (a * a) = a * (b * (a * a))) →
(∀ (a b : A), b * a * (a * a) = b * (a * a) * a) → IsJordan A | null | false |
CompactlySupportedContinuousMap.instInf._proof_2 | Mathlib.Topology.ContinuousMap.CompactlySupported | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : SemilatticeInf β] [inst_2 : Zero β]
[inst_3 : TopologicalSpace β] (f g : CompactlySupportedContinuousMap α β), HasCompactSupport (⇑f ⊓ ⇑g) | null | false |
_private.Mathlib.Algebra.Algebra.Bilinear.0.LinearMap.pow_mulLeft.match_1_1 | Mathlib.Algebra.Algebra.Bilinear | ∀ (motive : ℕ → Prop) (n : ℕ), (∀ (a : Unit), motive 0) → (∀ (n : ℕ), motive n.succ) → motive n | null | false |
_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_2 | Mathlib.Data.Nat.ChineseRemainder | ∀ {k : ℕ} {l : List ℕ}, k.Coprime l.prod = ∀ n ∈ l, k.Coprime n | null | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.