name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
IsApproximateAddSubgroup.addSubgroup | Mathlib.Combinatorics.Additive.ApproximateSubgroup | ∀ {G : Type u_1} [inst : AddGroup G] {S : Type u_2} [inst_1 : SetLike S G] [AddSubgroupClass S G] {H : S},
IsApproximateAddSubgroup 1 ↑H | true |
CommBialgCat.isoMk | Mathlib.Algebra.Category.CommBialgCat | {R : Type u} →
[inst : CommRing R] →
{X Y : Type v} →
{x : CommRing X} →
{x_1 : CommRing Y} →
{x_2 : Bialgebra R X} → {x_3 : Bialgebra R Y} → (X ≃ₐc[R] Y) → (CommBialgCat.of R X ≅ CommBialgCat.of R Y) | true |
RestrictedProduct.continuous_eval | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | ∀ {ι : Type u_1} {R : ι → Type u_2} {A : (i : ι) → Set (R i)} {𝓕 : Filter ι} [inst : (i : ι) → TopologicalSpace (R i)]
(i : ι), Continuous fun x => x i | true |
Std.DTreeMap.Raw.size_le_size_insertIfNew | Std.Data.DTreeMap.Raw.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap.Raw α β cmp} [Std.TransCmp cmp],
t.WF → ∀ {k : α} {v : β k}, t.size ≤ (t.insertIfNew k v).size | true |
Std.HashMap.values | Std.Data.HashMap.Basic | {α : Type u} → {β : Type v} → {x : BEq α} → {x_1 : Hashable α} → Std.HashMap α β → List β | true |
_private.Mathlib.Analysis.Convex.MetricSpace.0.continuous_convexComboPair_of_isBounded._simp_1_4 | Mathlib.Analysis.Convex.MetricSpace | ∀ {a b : Prop}, (¬(a ∧ b)) = (¬a ∨ ¬b) | false |
Std.HashMap.Raw.getKey?_filter_key | Std.Data.HashMap.RawLemmas | ∀ {α : Type u} {β : Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.HashMap.Raw α β} [EquivBEq α]
[LawfulHashable α] {f : α → Bool} {k : α},
m.WF → (Std.HashMap.Raw.filter (fun k x => f k) m).getKey? k = Option.filter f (m.getKey? k) | true |
instAddCommMonoidWeakDual._proof_11 | Mathlib.Topology.Algebra.Module.WeakDual | ∀ (𝕜 : Type u_1) (E : Type u_2) [inst : CommSemiring 𝕜] [inst_1 : TopologicalSpace 𝕜] [inst_2 : ContinuousAdd 𝕜]
[inst_3 : ContinuousConstSMul 𝕜 𝕜] [inst_4 : AddCommMonoid E] [inst_5 : Module 𝕜 E] [inst_6 : TopologicalSpace E],
autoParam
(∀ (n : ℕ) (x : WeakDual 𝕜 E),
instAddCommMonoidWeakDual._au... | false |
VSub.casesOn | Mathlib.Algebra.Notation.Defs | {G : Type u_1} →
{P : Type u_2} →
{motive : VSub G P → Sort u} → (t : VSub G P) → ((vsub : P → P → G) → motive { vsub := vsub }) → motive t | false |
Module.Basis.ofSplitExact._proof_3 | Mathlib.LinearAlgebra.Basis.Exact | ∀ {R : Type u_2} {M : Type u_4} {K : Type u_6} {P : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup K] [inst_3 : AddCommGroup P] [inst_4 : Module R M] [inst_5 : Module R K] [inst_6 : Module R P]
{f : K →ₗ[R] M} {g : M →ₗ[R] P} {s : M →ₗ[R] K},
s ∘ₗ f = LinearMap.id →
Function.Exact ... | false |
Std.IterM.mk.injEq | Init.Data.Iterators.Basic | ∀ {α : Type w} {m : Type w → Type w'} {β : Type w} (internalState internalState_1 : α),
({ internalState := internalState } = { internalState := internalState_1 }) = (internalState = internalState_1) | true |
AddAut.conj._proof_6 | Mathlib.Algebra.Group.End | ∀ {G : Type u_1} [inst : AddGroup G],
Additive.ofMul
{ toFun := fun h => 0 + h + -0, invFun := fun h => -0 + h + 0, left_inv := ⋯, right_inv := ⋯, map_add' := ⋯ } =
0 | false |
CategoryTheory.WithInitial.mapId | Mathlib.CategoryTheory.WithTerminal.Basic | (C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
CategoryTheory.WithInitial.map (CategoryTheory.Functor.id C) ≅
CategoryTheory.Functor.id (CategoryTheory.WithInitial C) | true |
Lean.Elab.Command.Scope.varUIds._default | Lean.Elab.Command.Scope | Array Lean.Name | false |
CategoryTheory.ShortComplex.Splitting.ofIso._proof_2 | Mathlib.Algebra.Homology.ShortComplex.Exact | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (s : S₁.Splitting) (e : S₁ ≅ S₂),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CategoryStruct.comp e.inv.τ₃ (CategoryTheory.CategoryStruct.comp s.s e.hom.τ₂)) S₂... | false |
Lean.Grind.Ring.neg_zsmul | Init.Grind.Ring.Basic | ∀ {α : Type u} [self : Lean.Grind.Ring α] (i : ℤ) (a : α), -i • a = -(i • a) | true |
Lean.Meta.RefinedDiscrTree.Key.labelledStar.noConfusion | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | {P : Sort u} →
{id id' : ℕ} →
Lean.Meta.RefinedDiscrTree.Key.labelledStar id = Lean.Meta.RefinedDiscrTree.Key.labelledStar id' →
(id = id' → P) → P | false |
HasFDerivAt.sub_const | Mathlib.Analysis.Calculus.FDeriv.Add | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
{f' : E →L[𝕜] F} {x : E} (c : F), HasFDerivAt f f' x → HasFDerivAt (fun x => f x - c) f' x | true |
Mathlib.Meta.NormNum.isNat_abs_nonneg | Mathlib.Tactic.NormNum.Abs | ∀ {α : Type u_1} [inst : Ring α] [inst_1 : Lattice α] [IsOrderedRing α] {a : α} {na : ℕ},
Mathlib.Meta.NormNum.IsNat a na → Mathlib.Meta.NormNum.IsNat |a| na | true |
Pi.single_mul_left_apply | Mathlib.Algebra.GroupWithZero.Pi | ∀ {ι : Type u_1} {α : ι → Type u_2} [inst : (i : ι) → MulZeroClass (α i)] [inst_1 : DecidableEq ι] (i j : ι) (a : α i)
(f : (i : ι) → α i), Pi.single i (a * f i) j = Pi.single i a j * f j | true |
AddCommGroupWithOne.toNatCast | Mathlib.Data.Int.Cast.Defs | {R : Type u} → [self : AddCommGroupWithOne R] → NatCast R | true |
Affine.Simplex.centroid_reindex | Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid | ∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {m n : ℕ} (s : Affine.Simplex k P m) (e : Fin (m + 1) ≃ Fin (n + 1)),
(s.reindex e).centroid = s.centroid | true |
ENNReal.div_lt_top | Mathlib.Data.ENNReal.Inv | ∀ {x y : ENNReal}, x ≠ ⊤ → y ≠ 0 → x / y < ⊤ | true |
List.length_range | Init.Data.List.Range | ∀ {n : ℕ}, (List.range n).length = n | true |
Lean.Elab.Do.mkMonadicType | Lean.Elab.Do.Basic | Lean.Expr → Lean.Elab.Do.DoElabM Lean.Expr | true |
MeasureTheory.integral_union_eq_left_of_forall | Mathlib.MeasureTheory.Integral.Bochner.Set | ∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{s t : Set X} {μ : MeasureTheory.Measure X} {f : X → E},
MeasurableSet t → (∀ x ∈ t, f x = 0) → ∫ (x : X) in s ∪ t, f x ∂μ = ∫ (x : X) in s, f x ∂μ | true |
ModuleCat.linearOverField._proof_2 | Mathlib.Algebra.Category.ModuleCat.Algebra | ∀ {k : Type u_3} [inst : Field k] {A : Type u_2} [inst_1 : Ring A] [inst_2 : Algebra k A] (X Y Z : ModuleCat A) (r : k)
(f : X ⟶ Y) (g : Y ⟶ Z), CategoryTheory.CategoryStruct.comp (r • f) g = r • CategoryTheory.CategoryStruct.comp f g | false |
ContDiffWithinAt.sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E} {s : Set E}
{n : WithTop ℕ∞}, ContDiffWithinAt ℝ n f s x → ContDiffWithinAt ℝ n (fun x => Real.sinh (f x)) s x | true |
_private.Init.Data.Vector.Count.0.Vector.count_le_count_map._simp_1_1 | Init.Data.Vector.Count | ∀ {α : Type u_2} [inst : BEq α] [LawfulBEq α] {β : Type u_1} [inst_2 : BEq β] [LawfulBEq β] {xs : Array α} {f : α → β}
{x : α}, (Array.count x xs ≤ Array.count (f x) (Array.map f xs)) = True | false |
_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.mk.noConfusion | Lean.Meta.Tactic.Grind.Theorems | {α : Type} →
{P : Sort u} →
{smap : Lean.PHashMap Lean.Name (List α)} →
{origins erased : Lean.PHashSet Lean.Meta.Grind.Origin} →
{omap : Lean.PHashMap Lean.Meta.Grind.Origin (List α)} →
{smap' : Lean.PHashMap Lean.Name (List α)} →
{origins' erased' : Lean.PHashSet Lean.Meta.Gr... | false |
CategoryTheory.RigidCategory.ctorIdx | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | {C : Type u} →
{inst : CategoryTheory.Category.{v, u} C} →
{inst_1 : CategoryTheory.MonoidalCategory C} → CategoryTheory.RigidCategory C → ℕ | false |
Array.all_subtype | Init.Data.Array.Attach | ∀ {α : Type u_1} {stop : ℕ} {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → Bool} {g : α → Bool},
(∀ (x : α) (h : p x), f ⟨x, h⟩ = g x) → stop = xs.size → xs.all f 0 stop = xs.unattach.all g | true |
gcd_comm | Mathlib.Algebra.GCDMonoid.Basic | ∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (a b : α), gcd a b = gcd b a | true |
BoxIntegral.Box.instPartialOrder._proof_3 | Mathlib.Analysis.BoxIntegral.Box.Basic | ∀ {ι : Type u_1} (a b : BoxIntegral.Box ι), a < b ↔ a ≤ b ∧ ¬b ≤ a | false |
_private.Std.Data.ExtDHashMap.Lemmas.0.Std.ExtDHashMap.map_eq_empty_iff._simp_1_2 | Std.Data.ExtDHashMap.Lemmas | ∀ {a b : Bool}, (a = true ↔ b = true) = (a = b) | false |
groupHomology.H0π_comp_H0Iso_hom_assoc | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | ∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) {Z : ModuleCat k}
(h : (Rep.coinvariantsFunctor k G).obj A ⟶ Z),
CategoryTheory.CategoryStruct.comp (groupHomology.H0π A)
(CategoryTheory.CategoryStruct.comp (groupHomology.H0Iso A).hom h) =
CategoryTheory.CategoryStruct.comp ... | true |
Finsupp.support_indicator_subset | Mathlib.Data.Finsupp.Indicator | ∀ {ι : Type u_1} {α : Type u_2} [inst : Zero α] (s : Finset ι) (f : (i : ι) → i ∈ s → α),
↑(Finsupp.indicator s f).support ⊆ ↑s | true |
AddSubsemigroup.centerToAddOpposite._proof_4 | Mathlib.GroupTheory.Submonoid.Center | ∀ {M : Type u_1} [inst : Add M] (r : ↥(AddSubsemigroup.center Mᵃᵒᵖ)), AddOpposite.unop ↑r ∈ Set.addCenter M | false |
Substring.Raw.Valid.data_drop | Batteries.Data.String.Lemmas | ∀ {s : Substring.Raw}, s.Valid → ∀ (n : ℕ), (s.drop n).toString.toList = List.drop n s.toString.toList | true |
_private.Mathlib.MeasureTheory.Integral.IntervalAverage.0.exists_eq_interval_average_of_noAtoms._proof_1_1 | Mathlib.MeasureTheory.Integral.IntervalAverage | ∀ {a b : ℝ} ⦃x : ℝ⦄, min a b < x → x < max a b → x ∈ Set.uIoc a b | false |
_private.Mathlib.Algebra.Category.ModuleCat.Semi.0.SemimoduleCat.mk | Mathlib.Algebra.Category.ModuleCat.Semi | {R : Type u} →
[inst : Semiring R] →
(carrier : Type v) → [isAddCommMonoid : AddCommMonoid carrier] → [isModule : Module R carrier] → SemimoduleCat R | true |
SimplicialObject.Split.rec | Mathlib.AlgebraicTopology.SimplicialObject.Split | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{motive : SimplicialObject.Split C → Sort u} →
((X : CategoryTheory.SimplicialObject C) → (s : SimplicialObject.Splitting X) → motive { X := X, s := s }) →
(t : SimplicialObject.Split C) → motive t | false |
QuasiconcaveOn.dual | Mathlib.Analysis.Convex.Quasiconvex | ∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : LE β] [inst_4 : SMul 𝕜 E] {s : Set E} {f : E → β},
QuasiconcaveOn 𝕜 s f → QuasiconvexOn 𝕜 s (⇑OrderDual.toDual ∘ f) | true |
IsDedekindDomain.HeightOneSpectrum.under._proof_1 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | ∀ (A : Type u_1) [inst : CommRing A] {B : Type u_2} [inst_1 : CommRing B] [inst_2 : Algebra A B]
(w : IsDedekindDomain.HeightOneSpectrum B), (Ideal.under A w.asIdeal).IsPrime | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order.0.isStrictlyPositive_add._proof_1_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | ∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : A},
IsStrictlyPositive a ∧ 0 ≤ b ∨ 0 ≤ a ∧ IsStrictlyPositive b → IsStrictlyPositive (a + b) | false |
Std.ExtDTreeMap.Const.alter_eq_empty_iff | Std.Data.ExtDTreeMap.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {β : Type v} {t : Std.ExtDTreeMap α (fun x => β) cmp} [inst : Std.TransCmp cmp]
{k : α} {f : Option β → Option β},
Std.ExtDTreeMap.Const.alter t k f = ∅ ↔ (t = ∅ ∨ t.size = 1 ∧ k ∈ t) ∧ f (Std.ExtDTreeMap.Const.get? t k) = none | true |
Lean.Server.FileWorker.WorkerState.mk.injEq | Lean.Server.FileWorker | ∀ (doc : Lean.Server.FileWorker.EditableDocument) (reporterCancelTk : IO.CancelToken)
(importCachingTask? : Option (Lean.Server.ServerTask (Except IO.Error Lean.Server.FileWorker.AvailableImportsCache)))
(pendingRequests : Lean.Server.FileWorker.PendingRequestMap)
(rpcSessions : Std.TreeMap UInt64 (IO.Ref Lean.Se... | true |
Finset.gcd_congr | Mathlib.Algebra.GCDMonoid.Finset | ∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s₁ s₂ : Finset β}
{f g : β → α}, s₁ = s₂ → (∀ a ∈ s₂, f a = g a) → s₁.gcd f = s₂.gcd g | true |
Valuation.mem_nhds_iff | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_3}
[inst_2 : LinearOrderedCommGroupWithZero Γ₀] [inst_3 : TopologicalSpace R] [IsValuativeTopology R]
(v : Valuation R Γ₀) [v.Compatible] {s : Set R} {x : R}, s ∈ nhds x ↔ ∃ γ, {z | v.restrict (z - x) < ↑γ} ⊆ s | true |
_private.Mathlib.NumberTheory.ModularForms.QExpansion.0.ModularFormClass.qExpansion_coeff_eq_intervalIntegral._simp_1_7 | Mathlib.NumberTheory.ModularForms.QExpansion | (Real.pi = 0) = False | false |
Std.TreeMap.getKeyD_insert_self | Std.Data.TreeMap.Lemmas | ∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.TreeMap α β cmp} [Std.TransCmp cmp] {a fallback : α}
{b : β}, (t.insert a b).getKeyD a fallback = a | true |
TopCat.ι₁_fst_assoc | Mathlib.Topology.Category.TopCat.Monoidal | ∀ (X : TopCat) {Z : TopCat} (h : X ⟶ Z),
CategoryTheory.CategoryStruct.comp TopCat.ι₁
(CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.fst X TopCat.I) h) =
h | true |
List.length_mapFinIdx | Init.Data.List.MapIdx | ∀ {α : Type u_1} {β : Type u_2} {as : List α} {f : (i : ℕ) → α → i < as.length → β}, (as.mapFinIdx f).length = as.length | true |
Subalgebra.normedCommRing._proof_1 | Mathlib.Analysis.Normed.Ring.Basic | ∀ {𝕜 : Type u_2} [inst : CommRing 𝕜] {E : Type u_1} [inst_1 : NormedCommRing E] [inst_2 : Algebra 𝕜 E]
(s : Subalgebra 𝕜 E) {x y : ↥s}, dist x y = 0 → x = y | false |
RelSeries.head_fromListIsChain | Mathlib.Order.RelSeries | ∀ {α : Type u_1} {r : SetRel α α} (l : List α) (l_ne_nil : l ≠ []) (hl : List.IsChain (fun x1 x2 => (x1, x2) ∈ r) l),
(RelSeries.fromListIsChain l l_ne_nil hl).head = l.head l_ne_nil | true |
_private.Mathlib.Tactic.Hint.0.Mathlib.Tactic.Hint._aux_Mathlib_Tactic_Hint___elabRules_Mathlib_Tactic_Hint_registerHintStx_1._sparseCasesOn_1 | Mathlib.Tactic.Hint | {α : Type u} →
{motive : Option α → Sort u_1} →
(t : Option α) → ((val : α) → motive (some val)) → (Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t | false |
Graph.IsLoopAt.mono | Mathlib.Combinatorics.Graph.Subgraph | ∀ {α : Type u_1} {β : Type u_2} {x : α} {e : β} {G H : Graph α β}, H ≤ G → H.IsLoopAt e x → G.IsLoopAt e x | true |
_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.take.match_1.splitter | Mathlib.Data.Seq.Basic | {α : Type u_1} →
(motive : ℕ → Stream'.Seq α → Sort u_2) →
(x : ℕ) →
(x_1 : Stream'.Seq α) →
((x : Stream'.Seq α) → motive 0 x) → ((n : ℕ) → (s : Stream'.Seq α) → motive n.succ s) → motive x x_1 | true |
ExteriorAlgebra.ι_inj._simp_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | ∀ (R : Type u1) [inst : CommRing R] {M : Type u2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] (x y : M),
((ExteriorAlgebra.ι R) x = (ExteriorAlgebra.ι R) y) = (x = y) | false |
CategoryTheory.NatTrans.leftOpWhiskerRight_assoc | Mathlib.CategoryTheory.Opposites | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F G : CategoryTheory.Functor C Dᵒᵖ} {E : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} E]
{H : CategoryTheory.Functor E C} (α : F ⟶ G) {Z : CategoryTheory.Functor Eᵒᵖ D} (h : (H.comp F).... | true |
edist_nndist | Mathlib.Topology.MetricSpace.Pseudo.Defs | ∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), edist x y = ↑(nndist x y) | true |
linearOrderOfSTO._proof_1 | Mathlib.Order.RelClasses | ∀ {α : Type u_1} (r : α → α → Prop) [IsStrictTotalOrder α r] (x y : α), ¬r y x ↔ x = y ∨ r x y | false |
Lean.Expr.proj.elim | Lean.Expr | {motive : Lean.Expr → Sort u} →
(t : Lean.Expr) →
t.ctorIdx = 11 →
((typeName : Lean.Name) → (idx : ℕ) → (struct : Lean.Expr) → motive (Lean.Expr.proj typeName idx struct)) →
motive t | false |
CategoryTheory.PreZeroHypercoverFamily._sizeOf_inst | Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily | (C : Type u) →
{inst : CategoryTheory.Category.{v, u} C} → [SizeOf C] → SizeOf (CategoryTheory.PreZeroHypercoverFamily C) | false |
Lean.Lsp.InitializationOptions.ctorIdx | Lean.Data.Lsp.InitShutdown | Lean.Lsp.InitializationOptions → ℕ | false |
instDecidableIrrationalSqrtOfNatReal | Mathlib.NumberTheory.Real.Irrational | {n : ℕ} → [inst : n.AtLeastTwo] → Decidable (Irrational √(OfNat.ofNat n)) | true |
ZeroAtInftyContinuousMap.rec | Mathlib.Topology.ContinuousMap.ZeroAtInfty | {α : Type u} →
{β : Type v} →
[inst : TopologicalSpace α] →
[inst_1 : Zero β] →
[inst_2 : TopologicalSpace β] →
{motive : ZeroAtInftyContinuousMap α β → Sort u_1} →
((toContinuousMap : C(α, β)) →
(zero_at_infty' : Filter.Tendsto toContinuousMap.toFun (Filter.coc... | false |
Submonoid.closure_insert_one | Mathlib.Algebra.Group.Submonoid.Basic | ∀ {M : Type u_1} [inst : MulOneClass M] (s : Set M), Submonoid.closure (insert 1 s) = Submonoid.closure s | true |
Std.DHashMap.Const.size_le_size_insertMany_list | Std.Data.DHashMap.Lemmas | ∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {β : Type v} {m : Std.DHashMap α fun x => β} [EquivBEq α]
[LawfulHashable α] {l : List (α × β)}, m.size ≤ (Std.DHashMap.Const.insertMany m l).size | true |
AdjoinRoot.instCommRing | Mathlib.RingTheory.AdjoinRoot | {R : Type u_1} → [inst : CommRing R] → (f : Polynomial R) → CommRing (AdjoinRoot f) | true |
Valued.instLinearOrderedCommGroupWithZeroValueGroup₀ValuationV | Mathlib.Topology.Algebra.Valued.ValuedField | {K : Type u_1} →
[inst : Field K] →
{Γ₀ : Type u_2} →
[inst_1 : LinearOrderedCommGroupWithZero Γ₀] →
[hv : Valued K Γ₀] → LinearOrderedCommGroupWithZero (MonoidWithZeroHom.ValueGroup₀ Valued.v) | true |
MeasurableSet.image_of_measurable_injOn | Mathlib.MeasureTheory.Constructions.Polish.Basic | ∀ {γ : Type u_3} {α : Type u_4} [inst : MeasurableSpace α] {s : Set γ} {f : γ → α}
[MeasurableSpace.CountablySeparated α] [inst_2 : MeasurableSpace γ] [StandardBorelSpace γ],
MeasurableSet s → Measurable f → Set.InjOn f s → MeasurableSet (f '' s) | true |
RelEmbedding.recOn | Mathlib.Order.RelIso.Basic | {α : Type u_5} →
{β : Type u_6} →
{r : α → α → Prop} →
{s : β → β → Prop} →
{motive : r ↪r s → Sort u} →
(t : r ↪r s) →
((toEmbedding : α ↪ β) →
(map_rel_iff' : ∀ {a b : α}, s (toEmbedding a) (toEmbedding b) ↔ r a b) →
motive { toEmbedding := t... | false |
CategoryTheory.Limits.WidePullbackShape.Hom.id.elim | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | {J : Type w} →
{motive : (a a_1 : CategoryTheory.Limits.WidePullbackShape J) → a.Hom a_1 → Sort u} →
{a a_1 : CategoryTheory.Limits.WidePullbackShape J} →
(t : a.Hom a_1) →
t.ctorIdx = 0 →
((X : CategoryTheory.Limits.WidePullbackShape J) →
motive X X (CategoryTheory.Limits.Wi... | false |
_private.Mathlib.Analysis.Complex.CanonicalDecomposition.0.Complex.canonicalFactor_ne_zero._simp_1_3 | Mathlib.Analysis.Complex.CanonicalDecomposition | ∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε : ℝ}, (y ∈ Metric.closedBall x ε) = (dist y x ≤ ε) | false |
Set.smul_set_univ | Mathlib.Algebra.Group.Action.Pointwise.Set.Basic | ∀ {α : Type u_2} {β : Type u_3} [inst : Group α] [inst_1 : MulAction α β] {a : α}, a • Set.univ = Set.univ | true |
UInt16.reduceLT | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | Lean.Meta.Simp.Simproc | true |
DilationEquiv.symm_bijective | Mathlib.Topology.MetricSpace.DilationEquiv | ∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y],
Function.Bijective DilationEquiv.symm | true |
Valuation.HasExtension.instIsLocalHomValuationInteger | Mathlib.RingTheory.Valuation.Extension | ∀ {R : Type u_1} [inst : CommRing R] {ΓR : Type u_6} [inst_1 : LinearOrderedCommGroupWithZero ΓR] {vR : Valuation R ΓR}
{S : Type u_9} {ΓS : Type u_10} [inst_2 : CommRing S] [inst_3 : LinearOrderedCommGroupWithZero ΓS]
[inst_4 : Algebra R S] [IsLocalHom (algebraMap R S)] {vS : Valuation S ΓS} [inst_6 : vR.HasExtens... | true |
Vector.instOrientedCmpCompareLex | Init.Data.Ord.Vector | ∀ {α : Type u_1} {cmp : α → α → Ordering} [Std.OrientedCmp cmp] {n : ℕ}, Std.OrientedCmp (Vector.compareLex cmp) | true |
DFinsupp.instDFunLike | Mathlib.Data.DFinsupp.Defs | {ι : Type u} → {β : ι → Type v} → [inst : (i : ι) → Zero (β i)] → DFunLike (Π₀ (i : ι), β i) ι β | true |
Mathlib.Meta.FunProp.Mor.Arg.noConfusionType | Mathlib.Tactic.FunProp.Mor | Sort u → Mathlib.Meta.FunProp.Mor.Arg → Mathlib.Meta.FunProp.Mor.Arg → Sort u | false |
SimpleGraph.isMaximalIndepSet_compl._simp_1 | Mathlib.Combinatorics.SimpleGraph.Clique | ∀ {α : Type u_3} {G : SimpleGraph α} (s : Finset α), Maximal Gᶜ.IsIndepSet ↑s = Maximal G.IsClique ↑s | false |
Std.Format.group.injEq | Init.Data.Format.Basic | ∀ (a : Std.Format) (behavior : Std.Format.FlattenBehavior) (a_1 : Std.Format) (behavior_1 : Std.Format.FlattenBehavior),
(a.group behavior = a_1.group behavior_1) = (a = a_1 ∧ behavior = behavior_1) | true |
RingQuot.instRing._proof_8 | Mathlib.Algebra.RingQuot | ∀ {R : Type u_1} [inst : Ring R] (r : R → R → Prop) (n : ℕ),
{ toQuot := Quot.mk (RingQuot.Rel r) ↑↑n } = { toQuot := Quot.mk (RingQuot.Rel r) ↑n } | false |
Sym2.rec.match_1 | Mathlib.Data.Sym.Sym2 | {α : Type u_1} → (motive : α × α → Sort u_2) → (x : α × α) → ((a b : α) → motive (a, b)) → motive x | false |
AlgebraicGeometry.isSmooth_isStableUnderBaseChange | Mathlib.AlgebraicGeometry.Morphisms.Smooth | CategoryTheory.MorphismProperty.IsStableUnderBaseChange @AlgebraicGeometry.Smooth | true |
_private.Mathlib.Algebra.Homology.Localization.0.HomotopyCategory.quotient_map_mem_quasiIso_iff._simp_1_1 | Mathlib.Algebra.Homology.Localization | ∀ {ι : Type u_1} {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {c : ComplexShape ι} {K L : HomologicalComplex C c}
[inst_2 : CategoryTheory.CategoryWithHomology C] (f : K ⟶ L), HomologicalComplex.quasiIso C c f = QuasiIso f | false |
ByteArray.forIn.loop._proof_4 | Init.Data.ByteArray.Basic | ∀ (as : ByteArray), ∀ i < as.size, i ≤ as.size | false |
AddMonoidAlgebra.opRingEquiv_symm_single | Mathlib.Algebra.MonoidAlgebra.Opposite | ∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : Add M] (r : Rᵐᵒᵖ) (x : Mᵃᵒᵖ),
AddMonoidAlgebra.opRingEquiv.symm (AddMonoidAlgebra.single x r) =
MulOpposite.op (AddMonoidAlgebra.single (AddOpposite.unop x) (MulOpposite.unop r)) | true |
CategoryTheory.Functor.mapHomologicalComplexIdIso._proof_2 | Mathlib.Algebra.Homology.Additive | ∀ {ι : Type u_1} (W₁ : Type u_3) [inst : CategoryTheory.Category.{u_2, u_3} W₁]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms W₁] (c : ComplexShape ι) (K : HomologicalComplex W₁ c) (i j : ι),
c.Rel i j →
CategoryTheory.CategoryStruct.comp
((fun x => CategoryTheory.Iso.refl ((((CategoryTheory.Functor.... | false |
cfcₙ.congr_simp | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | ∀ {R : Type u_3} {A : Type u_4} {p p_1 : A → Prop} (e_p : p = p_1) [inst : CommSemiring R] [inst_1 : Nontrivial R]
[inst_2 : StarRing R] [inst_3 : MetricSpace R] [inst_4 : IsTopologicalSemiring R] [inst_5 : ContinuousStar R]
[inst_6 : NonUnitalRing A] [inst_7 : StarRing A] [inst_8 : TopologicalSpace A] [inst_9 : Mo... | true |
Matrix.specialOrthogonalGroup | Mathlib.LinearAlgebra.UnitaryGroup | (n : Type u) →
[inst : DecidableEq n] → [inst_1 : Fintype n] → (R : Type v) → [inst_2 : CommRing R] → Submonoid (Matrix n n R) | true |
Equiv.mulOneClass | Mathlib.Algebra.Group.TransferInstance | {α : Type u_2} → {β : Type u_3} → α ≃ β → [MulOneClass β] → MulOneClass α | true |
_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_1 | Mathlib.Combinatorics.Matroid.Map | ∀ {α : Type u} {s : Set α}, (s ⊆ ∅) = (s = ∅) | false |
IsCyclotomicExtension.Rat.galEquivZMod.eq_1 | Mathlib.NumberTheory.NumberField.Cyclotomic.Galois | ∀ (n : ℕ) [inst : NeZero n] (K : Type u_1) [inst_1 : Field K] [inst_2 : NumberField K]
[hK : IsCyclotomicExtension {n} ℚ K],
IsCyclotomicExtension.Rat.galEquivZMod n K = IsCyclotomicExtension.autEquivPow K ⋯ | true |
_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem._proof_1_1 | Mathlib.Data.List.Sort | ∀ {α : Type u_1} {r : α → α → Prop} [inst : DecidableRel r] [inst_1 : DecidableEq α] {x : α},
(List.orderedInsert r x []).erase x = [] | false |
_private.Mathlib.RingTheory.Ideal.MinimalPrime.Basic.0.Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes.match_1_1 | Mathlib.RingTheory.Ideal.MinimalPrime.Basic | ∀ {R : Type u_2} [inst : CommSemiring R] {S : Type u_1} [inst_1 : CommRing S] [inst_2 : Algebra R S] {I : Ideal R}
{J : Ideal S} (q : Ideal S) (motive : q.IsPrime ∧ Ideal.map (algebraMap R S) I ⊔ J ≤ q → Prop)
(x : q.IsPrime ∧ Ideal.map (algebraMap R S) I ⊔ J ≤ q),
(∀ (left : q.IsPrime) (hleq : Ideal.map (algebra... | false |
Module.Basis.toMatrix_smul | Mathlib.LinearAlgebra.Matrix.Basis | ∀ {ι : Type u_1} {R₁ : Type u_9} {S : Type u_10} [inst : CommSemiring R₁] [inst_1 : Semiring S] [inst_2 : Algebra R₁ S]
[inst_3 : Fintype ι] [inst_4 : DecidableEq ι] (x : S) (b : Module.Basis ι R₁ S) (w : ι → S),
b.toMatrix (x • w) = (Algebra.leftMulMatrix b) x * b.toMatrix w | true |
ENNReal.ofReal_essSup | Mathlib.MeasureTheory.Function.EssSup | ∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) f →
Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) (MeasureTheory.ae μ) f →
ENNReal.ofReal (essSup f μ) = essSup (fun a => ENNReal.ofReal (f a)) μ | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.