name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Tactic.Linter.FlexibleLinter.0.Mathlib.Linter.Flexible.Stained.name | Mathlib.Tactic.Linter.FlexibleLinter | Lean.Name → Mathlib.Linter.Flexible.Stained✝ | true |
_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion.0.Tactic.ComputeAsymptotics.Seq.dist_le_half_iff._proof_1_1 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | (1 + 1).AtLeastTwo | false |
norm_inner_eq_norm_iff | Mathlib.Analysis.InnerProductSpace.Basic | ∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x y : E}, x ≠ 0 → y ≠ 0 → (‖inner 𝕜 x y‖ = ‖x‖ * ‖y‖ ↔ ∃ r, r ≠ 0 ∧ y = r • x) | true |
CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | ∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
[inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
(F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃))
(G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)) ... | true |
autAdjoinRootXPowSubCEquiv.eq_1 | Mathlib.FieldTheory.KummerExtension | ∀ {K : Type u} [inst : Field K] {n : ℕ} (hζ : (primitiveRoots n K).Nonempty) {a : K}
(H : Irreducible (Polynomial.X ^ n - Polynomial.C a)) [inst_1 : NeZero n],
autAdjoinRootXPowSubCEquiv hζ H =
{ toFun := (↑(autAdjoinRootXPowSubC n a)).toFun, invFun := AdjoinRootXPowSubCEquivToRootsOfUnity hζ H,
left_inv ... | true |
Char.val_ofOrdinal._proof_2 | Init.Data.Char.Ordinal | ∀ {f : Fin Char.numCodePoints}, ↑f + Char.numSurrogates < UInt32.size | false |
Polynomial.hasseDeriv_apply_one | Mathlib.Algebra.Polynomial.HasseDeriv | ∀ {R : Type u_1} [inst : Semiring R] (k : ℕ), 0 < k → (Polynomial.hasseDeriv k) 1 = 0 | true |
Std.ExtDTreeMap.minKey?_mem | Std.Data.ExtDTreeMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp]
{km : α}, t.minKey? = some km → km ∈ t | true |
Finset.coe_inj | Mathlib.Data.Finset.Defs | ∀ {α : Type u_1} {s₁ s₂ : Finset α}, ↑s₁ = ↑s₂ ↔ s₁ = s₂ | true |
legendreSym.quadratic_reciprocity | Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity | ∀ {p q : ℕ} [inst : Fact (Nat.Prime p)] [inst_1 : Fact (Nat.Prime q)],
p ≠ 2 → q ≠ 2 → p ≠ q → legendreSym q ↑p * legendreSym p ↑q = (-1) ^ (p / 2 * (q / 2)) | true |
Finset.op_vadd_finset_vadd_eq_vadd_vadd_finset | Mathlib.Algebra.Group.Pointwise.Finset.Scalar | ∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : DecidableEq β] [inst_1 : DecidableEq γ] [inst_2 : VAdd αᵃᵒᵖ β]
[inst_3 : VAdd β γ] [inst_4 : VAdd α γ] (a : α) (s : Finset β) (t : Finset γ),
(∀ (a : α) (b : β) (c : γ), (AddOpposite.op a +ᵥ b) +ᵥ c = b +ᵥ a +ᵥ c) → (AddOpposite.op a +ᵥ s) +ᵥ t = s +ᵥ a +ᵥ t | true |
_private.Mathlib.Analysis.Convex.Function.0.neg_strictConvexOn_iff._simp_1_2 | Mathlib.Analysis.Convex.Function | ∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddRightStrictMono α] {a b c : α}, (a + -b < c) = (a < c + b) | false |
_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.span_singleton_mul_eq_span_singleton_mul._simp_1_2 | Mathlib.RingTheory.Ideal.Operations | ∀ {R : Type u} [inst : CommSemiring R] {x y : R} {I J : Ideal R},
(Ideal.span {x} * I ≤ Ideal.span {y} * J) = ∀ zI ∈ I, ∃ zJ ∈ J, x * zI = y * zJ | false |
Real.range_arctan | Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan | Set.range Real.arctan = Set.Ioo (-(Real.pi / 2)) (Real.pi / 2) | true |
Lean.Elab.Term.elabCoeSortNotation._regBuiltin.Lean.Elab.Term.elabCoeSortNotation.declRange_3 | Lean.Elab.BuiltinNotation | IO Unit | false |
Lean.Meta.Grind.Arith.CommRing.EqCnstrProof.brecOn.eq | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | ∀ {motive_1 : Lean.Meta.Grind.Arith.CommRing.EqCnstr → Sort u}
{motive_2 : Lean.Meta.Grind.Arith.CommRing.EqCnstrProof → Sort u} (t : Lean.Meta.Grind.Arith.CommRing.EqCnstrProof)
(F_1 : (t : Lean.Meta.Grind.Arith.CommRing.EqCnstr) → t.below → motive_1 t)
(F_2 : (t : Lean.Meta.Grind.Arith.CommRing.EqCnstrProof) → ... | true |
AddMonoidHom.transfer_def | Mathlib.GroupTheory.Transfer | ∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {A : Type u_2} [inst_1 : AddCommGroup A] (ϕ : ↥H →+ A)
(T : H.LeftTransversal) [inst_2 : H.FiniteIndex] (g : G),
ϕ.transfer g = AddSubgroup.leftTransversals.diff ϕ T (g +ᵥ T) | true |
_private.Mathlib.LinearAlgebra.AffineSpace.Pointwise.0.AffineSubspace.pointwise_vadd_top._simp_1_1 | Mathlib.LinearAlgebra.AffineSpace.Pointwise | ∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β] (g : α) {x y : β},
(g +ᵥ x = y) = (x = -g +ᵥ y) | false |
Std.HashMap.getKey?_union | 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]
{k : α}, (m₁ ∪ m₂).getKey? k = (m₂.getKey? k).or (m₁.getKey? k) | true |
WithTop.continuousOn_untopD | Mathlib.Topology.Order.WithTop | ∀ {ι : Type u_1} [inst : LinearOrder ι] [inst_1 : TopologicalSpace ι] [inst_2 : OrderTopology ι] (d : ι),
ContinuousOn (WithTop.untopD d) {a | a ≠ ⊤} | true |
ENNReal.orderIsoUnitIntervalBirational | Mathlib.Data.ENNReal.Inv | ENNReal ≃o ↑(Set.Icc 0 1) | true |
Homeomorph.Set.prod._proof_1 | Mathlib.Topology.Homeomorph.Lemmas | ∀ {X : Type u_1} {Y : Type u_2} (s : Set X) (t : Set Y) (x : { x // x ∈ s ×ˢ t }), (↑x).1 ∈ s | false |
SemiRingCat.limitSemiring._proof_18 | Mathlib.Algebra.Category.Ring.Limits | ∀ {J : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} J] (F : CategoryTheory.Functor J SemiRingCat)
[inst_1 : Small.{u_2, max u_2 u_3} ↑(F.comp (CategoryTheory.forget SemiRingCat)).sections]
(a : (CategoryTheory.Limits.Types.Small.limitCone (F.comp (CategoryTheory.forget SemiRingCat))).pt), a * 0 = 0 | false |
DividedPowers.SubDPIdeal.mk.congr_simp | Mathlib.RingTheory.DividedPowers.SubDPIdeal | ∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} {hI : DividedPowers I} (carrier carrier_1 : Ideal A)
(e_carrier : carrier = carrier_1) (isSubideal : carrier ≤ I)
(dpow_mem : ∀ (n : ℕ), n ≠ 0 → ∀ j ∈ carrier, hI.dpow n j ∈ carrier),
{ carrier := carrier, isSubideal := isSubideal, dpow_mem := dpow_mem } =
... | true |
SSet.PtSimplex | Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | (X : SSet) → ℕ → X.obj (Opposite.op { len := 0 }) → Type u | true |
_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone.0.NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iff.match_1_6 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | ∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
(a b : ↑(NumberField.mixedEmbedding.fundamentalCone.integerSet K)) (motive : (∃ ζ, ↑ζ • ↑a = ↑b) → Prop)
(x : ∃ ζ, ↑ζ • ↑a = ↑b),
(∀ (u : (NumberField.RingOfIntegers K)ˣ) (property : u ∈ NumberField.Units.torsion K) (h : ↑⟨u, property⟩ • ↑a = ↑b),
m... | false |
AlgebraicTopology.map_alternatingFaceMapComplex | Mathlib.AlgebraicTopology.AlternatingFaceMapComplex | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {D : Type u_2}
[inst_2 : CategoryTheory.Category.{v_2, u_2} D] [inst_3 : CategoryTheory.Preadditive D]
(F : CategoryTheory.Functor C D) [inst_4 : F.Additive],
(AlgebraicTopology.alternatingFaceMapComplex C).comp... | true |
iteratedDerivWithin_of_isOpen_eq_iterate | Mathlib.Analysis.Calculus.IteratedDeriv.Defs | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {s : Set 𝕜},
IsOpen s → Set.EqOn (iteratedDerivWithin n f s) (deriv^[n] f) s | true |
Lean.PersistentHashMap.Stats._sizeOf_inst | Lean.Data.PersistentHashMap | SizeOf Lean.PersistentHashMap.Stats | false |
IsometryEquiv.mk.noConfusion | Mathlib.Topology.MetricSpace.Isometry | {α : Type u} →
{β : Type v} →
{inst : PseudoEMetricSpace α} →
{inst_1 : PseudoEMetricSpace β} →
{P : Sort u_1} →
{toEquiv : α ≃ β} →
{isometry_toFun : Isometry toEquiv.toFun} →
{toEquiv' : α ≃ β} →
{isometry_toFun' : Isometry toEquiv'.toFun} →
... | false |
StateCpsT.runK_bind_pure | Init.Control.StateCps | ∀ {α σ : Type u} {m : Type u → Type v} {β γ : Type u} (a : α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ),
(pure a >>= f).runK s k = (f a).runK s k | true |
CategoryTheory.Functor.mapAddMon_map_hom | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {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 D]
(F : CategoryTheory.Functor C D) [inst_4 : F.LaxMonoidal] {X Y : CategoryTheory.AddMon C} (f : X ⟶ Y),
(... | true |
LieHom.toLinearMap_comp._simp_1 | Mathlib.Algebra.Lie.Basic | ∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} {L₃ : Type w₁} [inst : CommRing R] [inst_1 : LieRing L₁]
[inst_2 : LieAlgebra R L₁] [inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] [inst_5 : LieRing L₃]
[inst_6 : LieAlgebra R L₃] (f : L₂ →ₗ⁅R⁆ L₃) (g : L₁ →ₗ⁅R⁆ L₂), ↑f ∘ₗ ↑g = ↑(f.comp g) | false |
Std.Do.SPred.Tactic.instIsPureImpPureForall | Std.Do.SPred.DerivedLaws | ∀ {φ ψ : Prop} (σs : List (Type u_1)), Std.Do.SPred.Tactic.IsPure spred(⌜φ⌝ → ⌜ψ⌝) (φ → ψ) | true |
Equiv.pointReflection_midpoint_right | Mathlib.LinearAlgebra.AffineSpace.Midpoint | ∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : Invertible 2] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] (x y : P), (Equiv.pointReflection (midpoint R x y)) y = x | true |
BiheytingAlgebra.ctorIdx | Mathlib.Order.Heyting.Basic | {α : Type u_4} → BiheytingAlgebra α → ℕ | false |
_private.Mathlib.Analysis.Calculus.FDeriv.Const.0.differentiableAt_of_fderiv_injective._simp_1_2 | Mathlib.Analysis.Calculus.FDeriv.Const | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F}, fderiv 𝕜 f = fderivWithin 𝕜 f Set.univ | false |
AlgebraicGeometry.Scheme.residueFieldCongr | Mathlib.AlgebraicGeometry.ResidueField | {X : AlgebraicGeometry.Scheme} → {x y : ↥X} → x = y → (X.residueField x ≅ X.residueField y) | true |
CategoryTheory.MorphismProperty.HasLocalization.noConfusionType | Mathlib.CategoryTheory.Localization.HasLocalization | Sort u_1 →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{W : CategoryTheory.MorphismProperty C} →
W.HasLocalization →
{C' : Type u} →
[inst' : CategoryTheory.Category.{v, u} C'] →
{W' : CategoryTheory.MorphismProperty C'} → W'.HasLocalization → Sort ... | false |
Lean.Server.MonadCancellable.noConfusionType | Lean.Server.RequestCancellation | Sort u →
{m : Type → Type v} → Lean.Server.MonadCancellable m → {m' : Type → Type v} → Lean.Server.MonadCancellable m' → Sort u | false |
LinearMap.prod_eq_inf_comap | Mathlib.LinearAlgebra.Prod | ∀ {R : Type u} {M : Type v} {M₂ : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R M] [inst_4 : Module R M₂] (p : Submodule R M) (q : Submodule R M₂),
p.prod q = Submodule.comap (LinearMap.fst R M M₂) p ⊓ Submodule.comap (LinearMap.snd R M M₂) q | true |
Std.TreeSet.getD_eq_fallback | Std.Data.TreeSet.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.TreeSet α cmp} [Std.TransCmp cmp] {a fallback : α},
a ∉ t → t.getD a fallback = fallback | true |
LSeriesHasSum.smul | Mathlib.NumberTheory.LSeries.Linearity | ∀ {f : ℕ → ℂ} (c : ℂ) {s a : ℂ}, LSeriesHasSum f s a → LSeriesHasSum (c • f) s (c * a) | true |
CategoryTheory.WithTerminal.comp.match_1 | Mathlib.CategoryTheory.WithTerminal.Basic | {C : Type u_1} →
(motive : CategoryTheory.WithTerminal C → CategoryTheory.WithTerminal C → CategoryTheory.WithTerminal C → Sort u_2) →
(x x_1 x_2 : CategoryTheory.WithTerminal C) →
((_X _Y _Z : C) →
motive (CategoryTheory.WithTerminal.of _X) (CategoryTheory.WithTerminal.of _Y)
(Categor... | false |
Lean.Lsp.InitializationOptions.hasWidgets? | Lean.Data.Lsp.InitShutdown | Lean.Lsp.InitializationOptions → Option Bool | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point.0.WeierstrassCurve.Jacobian.Point.toAffine_some._simp_1_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | ∀ {R : Type r} (a b c : R), ![a, b, c] 0 = a | false |
Filter.Tendsto.atTop_of_add_le_const | Mathlib.Order.Filter.AtTopBot.Monoid | ∀ {α : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedCancelAddMonoid M]
{l : Filter α} {f g : α → M},
(∃ C, ∀ (x : α), g x ≤ C) → Filter.Tendsto (fun x => f x + g x) l Filter.atTop → Filter.Tendsto f l Filter.atTop | true |
groupCohomology.coboundaries₁_le_cocycles₁ | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | ∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{max u u_1, u, u} k G),
groupCohomology.coboundaries₁ A ≤ groupCohomology.cocycles₁ A | true |
Padic.limSeq | Mathlib.NumberTheory.Padics.PadicNumbers | {p : ℕ} → [inst : Fact (Nat.Prime p)] → CauSeq ℚ_[p] ⇑padicNormE → ℕ → ℚ | true |
Vector.eq_empty | Init.Data.Vector.Lemmas | ∀ {α : Type u_1} {xs : Vector α 0}, xs = #v[] | true |
_private.Mathlib.LinearAlgebra.ExteriorAlgebra.Grading.0.ExteriorAlgebra.ιMulti_span.match_1_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Grading | ∀ (R : Type u_1) (M : Type u_2) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {i : ℕ}
(motive : ↥(⋀[R]^i M) → Prop) (hm : ↥(⋀[R]^i M)),
(∀ (m : ExteriorAlgebra R M) (hm : m ∈ ⋀[R]^i M), motive ⟨m, hm⟩) → motive hm | false |
_private.Lean.Elab.PreDefinition.WF.GuessLex.0.Lean.Elab.WF.GuessLex.explainMutualFailure.match_1 | Lean.Elab.PreDefinition.WF.GuessLex | (motive : Array (Array String) × String → Sort u_1) →
(x : Array (Array String) × String) →
((headerss : Array (Array String)) → (footer : String) → motive (headerss, footer)) → motive x | false |
Lean.Meta.instReduceEvalUInt64_qq | Qq.ForLean.ReduceEval | Lean.Meta.ReduceEval UInt64 | true |
Std.Iterators.Types.Zip.right | Std.Data.Iterators.Combinators.Monadic.Zip | {α₁ : Type w} →
{m : Type w → Type w'} →
{β₁ : Type w} →
[inst : Std.Iterator α₁ m β₁] → {α₂ β₂ : Type w} → Std.Iterators.Types.Zip α₁ m α₂ β₂ → Std.IterM m β₂ | true |
Vector.eraseIdx_append_of_lt_size._proof_2 | Init.Data.Vector.Erase | ∀ {n k : ℕ}, k < n → n - 1 + n = n + n - 1 | false |
_private.Lean.Meta.Sym.Simp.EvalGround.0.Lean.Meta.Sym.Simp.evalUnaryBitVec'.match_1 | Lean.Meta.Sym.Simp.EvalGround | (motive : OptionT Id Lean.Meta.Sym.BitVecValue → Sort u_1) →
(x : OptionT Id Lean.Meta.Sym.BitVecValue) →
((a : Lean.Meta.Sym.BitVecValue) → motive (some a)) →
((x : OptionT Id Lean.Meta.Sym.BitVecValue) → motive x) → motive x | false |
Matrix.IsAdjMatrix.toGraph_adj | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | ∀ {α : Type u_1} {V : Type u_2} {A : Matrix V V α} [inst : MulZeroOneClass α] [inst_1 : Nontrivial α]
(h : A.IsAdjMatrix) (i j : V), h.toGraph.Adj i j = (A i j = 1) | true |
Function.Surjective.moduleLeft._proof_3 | Mathlib.Algebra.Module.RingHom | ∀ {R : Type u_3} {S : Type u_2} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Semiring S] [inst_4 : SMul S M] (f : R →+* S) (hf : Function.Surjective ⇑f)
(hsmul : ∀ (c : R) (x : M), f c • x = c • x) (y₁ y₂ : S) (x : M), (y₁ + y₂) • x = y₁ • x + y₂ • x | false |
Std.HashMap.getKeyD_alter_self | Std.Data.HashMap.Lemmas | ∀ {α : Type u} {β : Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.HashMap α β} [EquivBEq α] [LawfulHashable α]
[Inhabited α] {k fallback : α} {f : Option β → Option β},
(m.alter k f).getKeyD k fallback = if (f m[k]?).isSome = true then k else fallback | true |
TopModuleCat.isColimitCoker._proof_4 | Mathlib.Algebra.Category.ModuleCat.Topology.Homology | ∀ {R : Type u_1} [inst : Ring R] [inst_1 : TopologicalSpace R] {M N : TopModuleCat R} (φ : M ⟶ N)
(s : CategoryTheory.Limits.CokernelCofork φ), ContinuousSMul R ↑s.1.toModuleCat | false |
ValuationRing.iff_dvd_total | Mathlib.RingTheory.Valuation.ValuationRing | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R], ValuationRing R ↔ Std.Total fun x1 x2 => x1 ∣ x2 | true |
disjointed_add_one | Mathlib.Algebra.Order.Disjointed | ∀ {α : Type u_1} {ι : Type u_2} [inst : GeneralizedBooleanAlgebra α] [inst_1 : LinearOrder ι]
[inst_2 : LocallyFiniteOrderBot ι] [inst_3 : Add ι] [inst_4 : One ι] [SuccAddOrder ι] [NoMaxOrder ι] (f : ι → α)
(i : ι), disjointed f (i + 1) = f (i + 1) \ (partialSups f) i | true |
MulEquiv.mapSubgroup.eq_1 | Mathlib.Algebra.Group.Subgroup.Map | ∀ {G : Type u_1} [inst : Group G] {H : Type u_6} [inst_1 : Group H] (f : G ≃* H),
f.mapSubgroup =
{ toFun := Subgroup.map ↑f, invFun := Subgroup.map ↑f.symm, left_inv := ⋯, right_inv := ⋯, map_rel_iff' := ⋯ } | true |
Lean.Lsp.ShowDocumentClientCapabilities | Lean.Data.Lsp.Capabilities | Type | true |
_private.Mathlib.Order.Partition.Finpartition.0.Finpartition.exists_le_of_le._proof_1_2 | Mathlib.Order.Partition.Finpartition | ∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a b : α} {P Q : Finpartition a},
(∀ p ∈ P.parts, ∃ q ∈ Q.parts.erase b, p ≤ q) → P.parts.sup id ≤ (Q.parts.erase b).sup id | false |
_private.Mathlib.LinearAlgebra.Dimension.Finite.0.Module.finite_finsupp_iff._simp_1_4 | Mathlib.LinearAlgebra.Dimension.Finite | ∀ {α : Type u_1}, (¬Subsingleton α) = Nontrivial α | false |
SimpleGraph.Finsubgraph.coe_compl._simp_1 | Mathlib.Combinatorics.SimpleGraph.Finsubgraph | ∀ {V : Type u} {G : SimpleGraph V} [inst : Finite V] (G' : G.Finsubgraph), (↑G')ᶜ = ↑G'ᶜ | false |
MeasureTheory.Measure.isOpenPosMeasure_smul | Mathlib.MeasureTheory.Measure.OpenPos | ∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure]
{c : ENNReal}, c ≠ 0 → (c • μ).IsOpenPosMeasure | true |
_private.Mathlib.CategoryTheory.NatTrans.0.CategoryTheory.NatTrans.ext.match_1 | Mathlib.CategoryTheory.NatTrans | ∀ {C : Type u_3} {inst : CategoryTheory.Category.{u_1, u_3} C} {D : Type u_4}
{inst_1 : CategoryTheory.Category.{u_2, u_4} D} {F G : CategoryTheory.Functor C D}
(motive : CategoryTheory.NatTrans F G → Prop) (h : CategoryTheory.NatTrans F G),
(∀ (app : (X : C) → F.obj X ⟶ G.obj X)
(naturality :
autoP... | false |
CategoryTheory.Localization.instHasSmallLocalizedHomObjShiftFunctor | Mathlib.CategoryTheory.Localization.SmallShiftedHom | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {M : Type w'}
[inst_1 : AddMonoid M] [inst_2 : CategoryTheory.HasShift C M] (X Y : C)
[CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] (m : M),
CategoryTheory.Localization.HasSmallLocalizedHom W X ... | true |
Lean.Meta.Hint.Suggestion | Lean.Meta.Hint | Type | true |
_private.Mathlib.MeasureTheory.Function.LpSpace.Basic.0.MeasureTheory.Lp.instNormedAddCommGroup._simp_3 | Mathlib.MeasureTheory.Function.LpSpace.Basic | ∀ {r q : NNReal}, (↑r ≤ ↑q) = (r ≤ q) | false |
Quaternion.instRing._proof_45 | Mathlib.Algebra.Quaternion | ∀ {R : Type u_1} [inst : CommRing R],
autoParam (∀ (n : ℕ), IntCast.intCast ↑n = ↑n) AddGroupWithOne.intCast_ofNat._autoParam | false |
OpenPartialHomeomorph.subtypeRestr_source | Mathlib.Topology.OpenPartialHomeomorph.Constructions | ∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) {s : TopologicalSpace.Opens X} (hs : Nonempty ↥s),
(e.subtypeRestr hs).source = Subtype.val ⁻¹' e.source | true |
AddMonoidAlgebra.mapDomain.eq_1 | Mathlib.Algebra.MonoidAlgebra.MapDomain | ∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] (f : M → N) (x : AddMonoidAlgebra R M),
AddMonoidAlgebra.mapDomain f x = Finsupp.mapDomain f x | true |
_private.Lean.Elab.PatternVar.0.Lean.Elab.Term.CollectPatternVars.collect.processCtorApp._sparseCasesOn_1 | Lean.Elab.PatternVar | {motive : Lean.Elab.Term.Arg → Sort u} →
(t : Lean.Elab.Term.Arg) →
((val : Lean.Syntax) → motive (Lean.Elab.Term.Arg.stx val)) → (Nat.hasNotBit 1 t.ctorIdx → motive t) → motive t | false |
Int.Linear.orOver_one | Init.Data.Int.Linear | ∀ {p : ℕ → Prop}, Int.Linear.OrOver 1 p → p 0 | true |
CategoryTheory.GlueData.mapGlueData._proof_6 | Mathlib.CategoryTheory.GlueData | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} C] {C' : Type u_2}
[inst_1 : CategoryTheory.Category.{u_1, u_2} C'] (D : CategoryTheory.GlueData C) (F : CategoryTheory.Functor C C')
[inst_2 : ∀ (i j k : D.J), CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan (D.f i j) (D.f i k)) F]
(i... | false |
_private.Mathlib.Order.Fin.Tuple.0.Fin.preimage_insertNth_Icc_of_notMem._simp_1_1 | Mathlib.Order.Fin.Tuple | ∀ {α : Type u} {β : Type v} {f : α → β} {s : Set β} {a : α}, (a ∈ f ⁻¹' s) = (f a ∈ s) | false |
_private.Mathlib.LinearAlgebra.Dimension.DivisionRing.0.rank_add_rank_split._simp_1_2 | Mathlib.LinearAlgebra.Dimension.DivisionRing | ∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
{f : M →ₛₗ[τ₁₂] M₂} {y : M}, (y ∈ f.ker) = (f y = 0) | false |
Hyperreal.Infinitesimal | Mathlib.Analysis.Real.Hyperreal | ℝ* → Prop | true |
WeierstrassCurve.Jacobian.fin3_def_ext | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic | ∀ {R : Type r} (a b c : R), ![a, b, c] 0 = a ∧ ![a, b, c] 1 = b ∧ ![a, b, c] 2 = c | true |
LinearPMap._sizeOf_inst | Mathlib.LinearAlgebra.LinearPMap | {R : Type u_1} →
{S : Type u_2} →
{inst : Ring R} →
{inst_1 : Ring S} →
(σ : R →+* S) →
(E : Type u_3) →
{inst_2 : AddCommGroup E} →
{inst_3 : Module R E} →
(F : Type u_4) →
{inst_4 : AddCommGroup F} →
{inst_5 ... | false |
hfdifferential._proof_2 | Mathlib.Geometry.Manifold.DerivationBundle | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_4} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_2}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddComm... | false |
_private.Aesop.Forward.State.0.Aesop.instBEqRawHyp.beq._sparseCasesOn_2 | Aesop.Forward.State | {motive : Aesop.RawHyp → Sort u} →
(t : Aesop.RawHyp) →
((subst : Aesop.Substitution) → motive (Aesop.RawHyp.patSubst subst)) →
(Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t | false |
Finpartition.casesOn | Mathlib.Order.Partition.Finpartition | {α : Type u_1} →
[inst : Lattice α] →
[inst_1 : OrderBot α] →
{a : α} →
{motive : Finpartition a → Sort u} →
(t : Finpartition a) →
((parts : Finset α) →
(supIndep : parts.SupIndep id) →
(sup_parts : parts.sup id = a) →
(bot... | false |
CategoryTheory.Bicategory.Adj.Hom.noConfusion | Mathlib.CategoryTheory.Bicategory.Adjunction.Adj | {P : Sort u_1} →
{B : Type u} →
{inst : CategoryTheory.Bicategory B} →
{a b : B} →
{t : CategoryTheory.Bicategory.Adj.Hom a b} →
{B' : Type u} →
{inst' : CategoryTheory.Bicategory B'} →
{a' b' : B'} →
{t' : CategoryTheory.Bicategory.Adj.Hom a' b'} ... | false |
Lean.Grind.CommRing.instBEqPoly.beq._sunfold | Init.Grind.Ring.CommSolver | Lean.Grind.CommRing.Poly → Lean.Grind.CommRing.Poly → Bool | false |
CategoryTheory.Adjunction.conesIsoComponentHom._proof_1 | Mathlib.CategoryTheory.Adjunction.Limits | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {D : Type u_6}
[inst_1 : CategoryTheory.Category.{u_5, u_6} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
(adj : F ⊣ G) {J : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} J] {K : CategoryTheory.Functor J D}
(X : Cᵒᵖ) (t... | false |
primorial_one | Mathlib.NumberTheory.Primorial | primorial 1 = 1 | true |
ENormedAddMonoid.enorm_eq_zero | Mathlib.Analysis.Normed.Group.Defs | ∀ {E : Type u_8} {inst : TopologicalSpace E} [self : ENormedAddMonoid E] (x : E), ‖x‖ₑ = 0 ↔ x = 0 | true |
Lean.Meta.Omega.OmegaConfig.mk | Init.Meta.Defs | Bool → Bool → Bool → Bool → Lean.Meta.Omega.OmegaConfig | true |
Std.ExtTreeMap.isSome_maxKey?_modify_eq_isSome | Std.Data.ExtTreeMap.Lemmas | ∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp] {k : α}
{f : β → β}, (t.modify k f).maxKey?.isSome = t.maxKey?.isSome | true |
CategoryTheory.ULift.equivalence_functor | Mathlib.CategoryTheory.Category.ULift | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C],
CategoryTheory.ULift.equivalence.functor = CategoryTheory.ULift.upFunctor | true |
Lean.ImportArtifacts.ofArray | Lean.Setup | Array System.FilePath → Lean.ImportArtifacts | true |
ContinuousLinearMap.flipMultilinear._proof_6 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | ∀ {𝕜 : Type u_3} {ι : Type u_4} {E : ι → Type u_5} {G : Type u_1} {G' : Type u_2} [inst : NontriviallyNormedField 𝕜]
[inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
[inst_3 : SeminormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] [inst_5 : SeminormedAddCommGroup G']
[i... | false |
MonCat.of | Mathlib.Algebra.Category.MonCat.Basic | (M : Type u) → [Monoid M] → MonCat | true |
Std.DTreeMap.Raw.getKey!_diff_of_not_mem_right | Std.Data.DTreeMap.Raw.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.DTreeMap.Raw α β cmp} [inst : Inhabited α]
[Std.TransCmp cmp], t₁.WF → t₂.WF → ∀ {k : α}, k ∉ t₂ → (t₁ \ t₂).getKey! k = t₁.getKey! k | true |
Int16.toBitVec_div | Init.Data.SInt.Lemmas | ∀ {a b : Int16}, (a / b).toBitVec = a.toBitVec.sdiv b.toBitVec | true |
Filter.not_bddBelow_of_tendsto_atBot | Mathlib.Order.Filter.AtTopBot.Basic | ∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {l : Filter α} [l.NeBot] {f : α → β} [NoMinOrder β],
Filter.Tendsto f l Filter.atBot → ¬BddBelow (Set.range f) | true |
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