name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
RestrictedProduct.mapAlong_continuous | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | ∀ {ι₁ : Type u_3} {ι₂ : Type u_4} (R₁ : ι₁ → Type u_5) (R₂ : ι₂ → Type u_6) [inst : (i : ι₁) → TopologicalSpace (R₁ i)]
[inst_1 : (i : ι₂) → TopologicalSpace (R₂ i)] {𝓕₁ : Filter ι₁} {𝓕₂ : Filter ι₂} {A₁ : (i : ι₁) → Set (R₁ i)}
{A₂ : (i : ι₂) → Set (R₂ i)} (f : ι₂ → ι₁) (hf : Filter.Tendsto f 𝓕₂ 𝓕₁) (φ : (j : ... | true |
_private.Mathlib.Algebra.Order.Group.Pointwise.Interval.0.Set.Ici_nsmul_eq.match_1_1 | Mathlib.Algebra.Order.Group.Pointwise.Interval | ∀ (motive : (x : ℕ) → x ≠ 0 → Prop) (x : ℕ) (x_1 : x ≠ 0),
(∀ (x : 1 ≠ 0), motive 1 x) → (∀ (n : ℕ) (x : n + 2 ≠ 0), motive n.succ.succ x) → motive x x_1 | false |
Int8.shiftLeft | Init.Data.SInt.Basic | Int8 → Int8 → Int8 | true |
_private.Mathlib.Analysis.Analytic.CPolynomialDef.0.HasFiniteFPowerSeriesOnBall.eq_partialSum._simp_1_1 | Mathlib.Analysis.Analytic.CPolynomialDef | ∀ {n m : ℕ}, (m ∈ Finset.range n) = (m < n) | false |
Quiver.zigzagSetoid.match_1 | Mathlib.Combinatorics.Quiver.ConnectedComponent | ∀ (V : Type u_1) [inst : Quiver V] {x y : V} (motive : Nonempty (Quiver.Path x y) → Prop)
(x_1 : Nonempty (Quiver.Path x y)), (∀ (p : Quiver.Path x y), motive ⋯) → motive x_1 | false |
_private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.rcases.match_8 | Lean.Elab.Tactic.RCases | (motive : Option Lean.Ident × Lean.Syntax → Sort u_1) →
(x : Option Lean.Ident × Lean.Syntax) →
((hName? : Option Lean.Ident) → (tgt : Lean.Syntax) → motive (hName?, tgt)) → motive x | false |
MeasureTheory.withDensityᵥ_add | Mathlib.MeasureTheory.VectorMeasure.WithDensity | ∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
[inst_1 : NormedSpace ℝ E] {f g : α → E},
MeasureTheory.Integrable f μ →
MeasureTheory.Integrable g μ → μ.withDensityᵥ (f + g) = μ.withDensityᵥ f + μ.withDensityᵥ g | true |
Set.fintypeOfFintypeImage | Mathlib.Data.Set.Finite.Basic | {α : Type u} →
{β : Type v} →
(s : Set α) → {f : α → β} → {g : β → Option α} → Function.IsPartialInv f g → [Fintype ↑(f '' s)] → Fintype ↑s | true |
_private.Mathlib.Geometry.Manifold.VectorField.LieBracket.0.VectorField.mpullbackWithin_mlieBracketWithin_aux | Mathlib.Geometry.Manifold.VectorField.LieBracket | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {H' : Type u_5} [inst_6 : TopologicalSp... | true |
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_map_hom | Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
(F :
CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
(CategoryTheory.Bicategory.Adj CategoryTheory.Cat))
(ι : Type u_1) [inst_1 : Unique ι] {X S : C} (f : X ⟶ S)
{X_1 Y : (CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj).t... | true |
AlgebraicGeometry.Scheme.range_fromSpecResidueField | Mathlib.AlgebraicGeometry.ResidueField | ∀ {X : AlgebraicGeometry.Scheme} (x : ↥X), Set.range ⇑(X.fromSpecResidueField x) = {x} | true |
MonoidAlgebra.mapDomainRingEquiv_apply | Mathlib.Algebra.MonoidAlgebra.MapDomain | ∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] [inst_1 : Monoid M] [inst_2 : Monoid N] (e : M ≃* N)
(x : MonoidAlgebra R M) (n : N), ((MonoidAlgebra.mapDomainRingEquiv R e) x) n = x (e.symm n) | true |
Filter.Germ.coeRingHom | Mathlib.Order.Filter.Germ.Basic | {α : Type u_1} → {R : Type u_5} → [inst : Semiring R] → (l : Filter α) → (α → R) →+* l.Germ R | true |
LSeries.logMul | Mathlib.NumberTheory.LSeries.Deriv | (ℕ → ℂ) → ℕ → ℂ | true |
_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.eq_zero_of_comapDomain_eq_zero._simp_1_2 | Mathlib.Data.Finsupp.Basic | ∀ {α : Type u_1} {s₁ s₂ : Finset α}, (s₁ = s₂) = ∀ (a : α), a ∈ s₁ ↔ a ∈ s₂ | false |
intervalIntegral.intervalIntegral_pos_of_pos_on | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | ∀ {f : ℝ → ℝ} {a b : ℝ},
IntervalIntegrable f MeasureTheory.volume a b → (∀ x ∈ Set.Ioo a b, 0 < f x) → a < b → 0 < ∫ (x : ℝ) in a..b, f x | true |
Std.instCoeDepAnyAsyncStreamOfAsyncStream | Std.Sync.StreamMap | {t α : Type} → {x : t} → [Std.Internal.Async.IO.AsyncStream t α] → CoeDep t x (Std.AnyAsyncStream α) | true |
List.forall₂_nil_left_iff._simp_1 | Mathlib.Data.List.Forall2 | ∀ {α : Type u_1} {β : Type u_2} {R : α → β → Prop} {l : List β}, List.Forall₂ R [] l = (l = []) | false |
AddMonoidAlgebra.nonAssocSemiring.eq_1 | Mathlib.Algebra.MonoidAlgebra.Defs | ∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddZeroClass M],
AddMonoidAlgebra.nonAssocSemiring =
{ toNonUnitalNonAssocSemiring := AddMonoidAlgebra.nonUnitalNonAssocSemiring, toOne := AddMonoidAlgebra.zero,
one_mul := ⋯, mul_one := ⋯, natCast := fun n => AddMonoidAlgebra.single 0 ↑n, natCas... | true |
_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_4 | Mathlib.Data.List.Lattice | ∀ {α : Type u_1} [inst : DecidableEq α] (a : α) (l₁ l₂ : List α),
(l₁.bagInter (l₂.erase a)).Sublist l₁ → (a :: l₁.bagInter (l₂.erase a)).Sublist (a :: l₁) | false |
CategoryTheory.ShortComplex.SnakeInput.mono_L₀_f | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
(S : CategoryTheory.ShortComplex.SnakeInput C) [CategoryTheory.Mono S.L₁.f], CategoryTheory.Mono S.L₀.f | true |
Localization.mk_eq_monoidOf_mk' | Mathlib.GroupTheory.MonoidLocalization.Basic | ∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M}, Localization.mk = (Localization.monoidOf S).mk' | true |
lt_add_iff_pos_left._simp_1 | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | ∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : LT α] [AddRightStrictMono α] [AddRightReflectLT α] (a : α) {b : α},
(a < b + a) = (0 < b) | false |
ContinuousMapZero.nonUnitalStarAlgHom_postcomp._proof_3 | Mathlib.Topology.ContinuousMap.ContinuousMapZero | ∀ (X : Type u_2) {M : Type u_4} {R : Type u_3} {S : Type u_1} [inst : Zero X] [inst_1 : CommSemiring M]
[inst_2 : TopologicalSpace X] [inst_3 : TopologicalSpace R] [inst_4 : TopologicalSpace S] [inst_5 : CommSemiring R]
[inst_6 : StarRing R] [inst_7 : IsTopologicalSemiring R] [inst_8 : CommSemiring S] [inst_9 : Sta... | false |
_private.Mathlib.Combinatorics.Colex.0.Finset.Colex.singleton_le_singleton._simp_1_1 | Mathlib.Combinatorics.Colex | ∀ {α : Type u_1} [inst : PartialOrder α] {s : Finset α} {a : α},
(toColex s ≤ toColex {a}) = ∀ b ∈ s, b ≤ a ∧ (a ∈ s → b = a) | false |
CategoryTheory.mono_iff_isIso_fst | Mathlib.CategoryTheory.Limits.EpiMono | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} {f : X ⟶ Y}
{c : CategoryTheory.Limits.PullbackCone f f} (hc : CategoryTheory.Limits.IsLimit c),
CategoryTheory.Mono f ↔ CategoryTheory.IsIso c.fst | true |
TwoUniqueProds.instForall | Mathlib.Algebra.Group.UniqueProds.Basic | ∀ {ι : Type u_2} (G : ι → Type u_1) [inst : (i : ι) → Mul (G i)] [∀ (i : ι), TwoUniqueProds (G i)],
TwoUniqueProds ((i : ι) → G i) | true |
Std.HashMap.Raw.mem_of_mem_filterMap | Std.Data.HashMap.RawLemmas | ∀ {α : Type u} {β : Type v} {γ : Type w} [inst : BEq α] [inst_1 : Hashable α] {m : Std.HashMap.Raw α β} [EquivBEq α]
[LawfulHashable α] {f : α → β → Option γ} {k : α}, m.WF → k ∈ Std.HashMap.Raw.filterMap f m → k ∈ m | true |
CategoryTheory.InducedWideCategory.congr_simp | Mathlib.CategoryTheory.Widesubcategory | ∀ {C : Type u₁} (D : Type u₂) [inst : CategoryTheory.Category.{v₁, u₂} D] (_F _F_1 : C → D),
_F = _F_1 →
∀ (_P _P_1 : CategoryTheory.MorphismProperty D) (e__P : _P = _P_1) [inst_1 : _P.IsMultiplicative],
CategoryTheory.InducedWideCategory D _F _P = CategoryTheory.InducedWideCategory D _F_1 _P_1 | true |
Lean.Meta.Grind.Arith.Linear.geAvoiding._unsafe_rec | Lean.Meta.Tactic.Grind.Arith.Linear.Search | ℚ → Array (ℚ × Lean.Meta.Grind.Arith.Linear.DiseqCnstr) → ℚ | false |
Std.HashMap.Raw.getElem?_insert | Std.Data.HashMap.RawLemmas | ∀ {α : Type u} {β : Type v} {m : Std.HashMap.Raw α β} [inst : BEq α] [inst_1 : Hashable α] [EquivBEq α]
[LawfulHashable α], m.WF → ∀ {k a : α} {v : β}, (m.insert k v)[a]? = if (k == a) = true then some v else m[a]? | true |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Unbounded.recv.match_1 | Std.Sync.Channel | {α : Type} →
(motive : Option α → Sort u_1) →
(__do_lift : Option α) → ((val : α) → motive (some val)) → ((x : Option α) → motive x) → motive __do_lift | false |
_private.Mathlib.Data.DFinsupp.Multiset.0.DFinsupp.toMultiset_le_toMultiset._simp_1_1 | Mathlib.Data.DFinsupp.Multiset | ∀ {α : Type u_1} [inst : DecidableEq α] {s t : Multiset α}, (s ≤ t) = (Multiset.toDFinsupp s ≤ Multiset.toDFinsupp t) | false |
_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.mkBaseNameCore.visit.eq_def | Lean.Elab.DeclNameGen | ∀ (e : Lean.Expr) (omitTopForall : optParam Bool false),
Lean.Elab.Command.NameGen.mkBaseNameCore.visit✝ e omitTopForall = do
let __do_lift ← get
if Std.HashSet.contains (Lean.Elab.Command.NameGen.MkNameState.seen✝ __do_lift) e = true then pure ""
else do
let s ← Lean.Elab.Command.NameGen.mkBase... | true |
_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.lt_trichotomy_rec._proof_2 | Mathlib.Data.DFinsupp.Lex | ∀ {ι : Type u_1} {α : ι → Type u_2} [inst : (i : ι) → Zero (α i)] [inst_1 : LinearOrder ι]
[inst_2 : (i : ι) → LinearOrder (α i)] (f g : Π₀ (i : ι), α i), (f.neLocus g).min = ⊤ → toLex f = toLex g | false |
Set.Definable.image_comp_equiv | Mathlib.ModelTheory.Definability | ∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {β : Type u_1}
{s : Set (β → M)}, A.Definable L s → ∀ (f : α ≃ β), A.Definable L ((fun g => g ∘ ⇑f) '' s) | true |
Std.ExtDTreeMap.Const.mem_toList_iff_get?_eq_some | 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]
[Std.LawfulEqCmp cmp] {k : α} {v : β},
(k, v) ∈ Std.ExtDTreeMap.Const.toList t ↔ Std.ExtDTreeMap.Const.get? t k = some v | true |
Lean.Meta.SolveByElim.saturateSymm | Lean.Meta.Tactic.SolveByElim | Bool → List Lean.Expr → Lean.MetaM (List Lean.Expr) | true |
ConvexCone.mem_mk | Mathlib.Geometry.Convex.Cone.Basic | ∀ {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : AddCommMonoid M]
[inst_3 : SMul R M] {s : Set M} {x : M} {h₁ : ∀ ⦃c : R⦄, 0 < c → ∀ ⦃x : M⦄, x ∈ s → c • x ∈ s}
{h₂ : ∀ ⦃x : M⦄, x ∈ s → ∀ ⦃y : M⦄, y ∈ s → x + y ∈ s}, x ∈ { carrier := s, smul_mem' := h₁, add_mem' := h₂ } ↔ x ∈ ... | true |
_private.Lean.Elab.Binders.0.Lean.Elab.Term.FunBinders.elabFunBinderViews | Lean.Elab.Binders | Array Lean.Elab.Term.BinderView →
ℕ → Lean.Elab.Term.FunBinders.State → Lean.Elab.TermElabM Lean.Elab.Term.FunBinders.State | true |
Nat.one_lt_succ_succ | Init.Data.Nat.Lemmas | ∀ (n : ℕ), 1 < n.succ.succ | true |
_private.Qq.Commands.0.Qq.mkLetFVarsFromValues | Qq.Commands | Array Lean.Expr → Lean.Expr → Lean.MetaM Lean.Expr | true |
Complex.isCauSeq_exp | Mathlib.Analysis.Complex.Exponential | ∀ (z : ℂ), IsCauSeq (fun x => ‖x‖) fun n => ∑ m ∈ Finset.range n, z ^ m / ↑m.factorial | true |
List.monotone_sum_take | Mathlib.Algebra.Order.BigOperators.Group.List | ∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [CanonicallyOrderedAdd M] (L : List M),
Monotone fun i => (List.take i L).sum | true |
AddMonoidAlgebra.smulZeroClass._proof_1 | Mathlib.Algebra.MonoidAlgebra.Defs | ∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] {A : Type u_3} [inst_1 : SMulZeroClass A R] (a : A), a • 0 = 0 | false |
CategoryTheory.Bicategory.Prod.snd_map₂ | Mathlib.CategoryTheory.Bicategory.Product | ∀ (B : Type u₁) [inst : CategoryTheory.Bicategory B] (C : Type u₂) [inst_1 : CategoryTheory.Bicategory C] {a b : B × C}
{f g : a ⟶ b} (a_1 : f ⟶ g), (CategoryTheory.Bicategory.Prod.snd B C).map₂ a_1 = a_1.2 | true |
ContinuousMap.Homotopy.ulift_apply | Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps | ∀ {X Y : TopCat} {f g : C(↑X, ↑Y)} (H : f.Homotopy g) (i : ULift.{u, 0} ↑unitInterval) (x : ↑X),
H.uliftMap (i, x) = H (i.down, x) | true |
Finsupp.coe_mk | Mathlib.Data.Finsupp.Defs | ∀ {α : Type u_1} {M : Type u_4} [inst : Zero M] (f : α → M) (s : Finset α) (h : ∀ (a : α), a ∈ s ↔ f a ≠ 0),
⇑{ support := s, toFun := f, mem_support_toFun := h } = f | true |
UInt16.ofNatTruncate_toNat | Init.Data.UInt.Lemmas | ∀ (n : UInt16), UInt16.ofNatTruncate n.toNat = n | true |
Int.getElem_toList_roo | Init.Data.Range.Polymorphic.IntLemmas | ∀ {m n : ℤ} {i : ℕ} (_h : i < (m<...n).toList.length), (m<...n).toList[i] = m + 1 + ↑i | true |
Rep.coinvariantsTensorIndInv._proof_2 | Mathlib.RepresentationTheory.Induced | ∀ {k : Type u_1} [inst : CommRing k] {G H : Type u_1} [inst_1 : Group G] [inst_2 : Group H] (φ : G →* H)
(A : Rep.{u_1, u_1, u_1} k G) (B : Rep.{u_1, u_1, u_1} k H),
SMulCommClass k k
(((CategoryTheory.MonoidalCategory.curriedTensor (Rep.{u_1, u_1, u_1} k H)).obj (Rep.ind φ A)).obj B).ρ.Coinvariants | false |
_private.Mathlib.Geometry.Manifold.MFDeriv.Basic.0.mdifferentiableWithinAt_congr_set'._simp_1_1 | Mathlib.Geometry.Manifold.MFDeriv.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}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddComm... | false |
_private.Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra.0.CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.ext.match_1 | Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | ∀ {C : Type u_5} {inst : CategoryTheory.Category.{u_3, u_5} C}
{F :
CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
(CategoryTheory.Bicategory.Adj CategoryTheory.Cat)}
{ι : Type u_1} {S : C} {X : ι → C} {f : (i : ι) → X i ⟶ S} {D₁ D₂ : F.DescentDataAsCoalgebra f}
(motive : D₁.Hom D₂ → ... | false |
Std.DTreeMap.Internal.Impl.length_keys | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {β : α → Type v} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α β} [Std.TransOrd α],
t.WF → t.keys.length = t.size | true |
_private.Aesop.RuleTac.Cases.0.Aesop.RuleTac.cases.go.match_10 | Aesop.RuleTac.Cases | (motive : Option (Array Lean.Meta.CasesSubgoal) → Sort u_1) →
(__discr : Option (Array Lean.Meta.CasesSubgoal)) →
((goals : Array Lean.Meta.CasesSubgoal) → motive (some goals)) →
((x : Option (Array Lean.Meta.CasesSubgoal)) → motive x) → motive __discr | false |
MeasureTheory.Measure.AbsolutelyContinuous.support_mono | Mathlib.MeasureTheory.Measure.Support | ∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] {μ ν : MeasureTheory.Measure X},
μ.AbsolutelyContinuous ν → μ.support ⊆ ν.support | true |
List.getLast._proof_1 | Init.Data.List.Basic | ∀ {α : Type u_1}, [] = [] | false |
_private.Mathlib.Tactic.TacticAnalysis.Declarations.0.Mathlib.TacticAnalysis.TerminalReplacementOutcome.error.noConfusion | Mathlib.Tactic.TacticAnalysis.Declarations | {P : Sort u} →
{stx : Lean.TSyntax `tactic} →
{msg : Lean.MessageData} →
{stx' : Lean.TSyntax `tactic} →
{msg' : Lean.MessageData} →
Mathlib.TacticAnalysis.TerminalReplacementOutcome.error✝ stx msg =
Mathlib.TacticAnalysis.TerminalReplacementOutcome.error✝¹ stx' msg' →
... | false |
DirectSum.GSemiring.casesOn | Mathlib.Algebra.DirectSum.Ring | {ι : Type u_1} →
{A : ι → Type u_2} →
[inst : AddMonoid ι] →
[inst_1 : (i : ι) → AddCommMonoid (A i)] →
{motive : DirectSum.GSemiring A → Sort u} →
(t : DirectSum.GSemiring A) →
([toGNonUnitalNonAssocSemiring : DirectSum.GNonUnitalNonAssocSemiring A] →
[toGOne :... | false |
_private.Lean.Elab.Tactic.Simp.0.Lean.Elab.Tactic.elabSimpArgs.match_13 | Lean.Elab.Tactic.Simp | (motive : Lean.Syntax × Lean.Elab.Tactic.ElabSimpArgResult → Sort u_1) →
(x : Lean.Syntax × Lean.Elab.Tactic.ElabSimpArgResult) →
((ref : Lean.Syntax) → (arg : Lean.Elab.Tactic.ElabSimpArgResult) → motive (ref, arg)) → motive x | false |
Std.Tactic.BVDecide.LRAT.Internal.lratChecker._unsafe_rec | Std.Tactic.BVDecide.LRAT.Internal.LRATChecker | {α : Type u_1} →
{β : Type u_2} →
{σ : Type u_3} →
[DecidableEq α] →
[inst : Std.Tactic.BVDecide.LRAT.Internal.Clause α β] →
[inst_1 : Std.Tactic.BVDecide.LRAT.Internal.Entails α σ] →
[Std.Tactic.BVDecide.LRAT.Internal.Formula α β σ] →
σ → List (Std.Tactic.BVDecid... | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.isEmpty_iff_forall_isSome_getEntry?.match_1_1 | Std.Data.Internal.List.Associative | ∀ {α : Type u_2} {β : α → Type u_1} (motive : List ((a : α) × β a) → Prop) (x : List ((a : α) × β a)),
(∀ (a : Unit), motive []) → (∀ (k : α) (v : β k) (l : List ((a : α) × β a)), motive (⟨k, v⟩ :: l)) → motive x | false |
Finset.piecewise | Mathlib.Data.Finset.Piecewise | {ι : Type u_1} →
{π : ι → Sort u_2} →
(s : Finset ι) → ((i : ι) → π i) → ((i : ι) → π i) → [(j : ι) → Decidable (j ∈ s)] → (i : ι) → π i | true |
AbstractSimplicialComplex.mk | Mathlib.AlgebraicTopology.SimplicialComplex.Basic | {ι : Type u_1} →
(toPreAbstractSimplicialComplex : PreAbstractSimplicialComplex ι) →
(∀ (v : ι), {v} ∈ toPreAbstractSimplicialComplex.faces) → AbstractSimplicialComplex ι | true |
PhragmenLindelof.eq_zero_on_quadrant_IV | Mathlib.Analysis.Complex.PhragmenLindelof | ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E},
DiffContOnCl ℂ f (Set.Ioi 0 ×ℂ Set.Iio 0) →
(∃ c < 2,
∃ B, f =O[Bornology.cobounded ℂ ⊓ Filter.principal (Set.Ioi 0 ×ℂ Set.Iio 0)] fun z => Real.exp (B * ‖z‖ ^ c)) →
(∀ (x : ℝ), 0 ≤ x → f ↑x = 0) → (∀ x ≤ 0, f (↑x... | true |
IsTopologicalRing.toIsSemitopologicalRing | Mathlib.Topology.Algebra.Ring.Basic | ∀ (R : Type u_2) [inst : TopologicalSpace R] [inst_1 : NonUnitalNonAssocRing R] [IsTopologicalRing R],
IsSemitopologicalRing R | true |
_private.Mathlib.Topology.Order.LeftRightLim.0.Monotone.leftLim_le._simp_1_4 | Mathlib.Topology.Order.LeftRightLim | ∀ {α : Type u_1} [inst : Preorder α] {b x : α}, (x ∈ Set.Iio b) = (x < b) | false |
Monotone.withTop_map | Mathlib.Order.WithBot | ∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → Monotone (WithTop.map f) | true |
npow_mul_comm | Mathlib.Algebra.Group.NatPowAssoc | ∀ {M : Type u_1} [inst : MulOneClass M] [inst_1 : Pow M ℕ] [NatPowAssoc M] (m n : ℕ) (x : M),
x ^ m * x ^ n = x ^ n * x ^ m | true |
MonCat.Colimits.quot_one | Mathlib.Algebra.Category.MonCat.Colimits | ∀ {J : Type v} [inst : CategoryTheory.Category.{u, v} J] (F : CategoryTheory.Functor J MonCat),
Quot.mk (⇑(MonCat.Colimits.colimitSetoid F)) MonCat.Colimits.Prequotient.one = 1 | true |
IsLocalHomeomorphOn.of_comp_left | Mathlib.Topology.IsLocalHomeomorph | ∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] {g : Y → Z} {f : X → Y} {s : Set X},
IsLocalHomeomorphOn (g ∘ f) s → IsLocalHomeomorphOn g (f '' s) → (∀ x ∈ s, ContinuousAt f x) → IsLocalHomeomorphOn f s | true |
AddChar.PrimitiveAddChar.char | Mathlib.NumberTheory.LegendreSymbol.AddCharacter | {R : Type u} →
[inst : CommRing R] →
{R' : Type v} →
[inst_1 : Field R'] → (self : AddChar.PrimitiveAddChar R R') → AddChar R (CyclotomicField (↑self.n) R') | true |
skyscraperSheafForgetAdjunction | Mathlib.Topology.Sheaves.Skyscraper | {X : TopCat} →
(p₀ : ↑X) →
[inst : (U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] →
{C : Type v} →
[inst_1 : CategoryTheory.Category.{u, v} C] →
[inst_2 : CategoryTheory.Limits.HasTerminal C] →
[inst_3 : CategoryTheory.Limits.HasColimits C] →
TopCat.Preshea... | true |
MulEquiv.coe_subgroupMap_apply | Mathlib.Algebra.Group.Subgroup.Map | ∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] (e : G ≃* G') (H : Subgroup G) (g : ↥H),
↑((e.subgroupMap H) g) = e ↑g | true |
Polynomial.expand_eq_zero | Mathlib.Algebra.Polynomial.Expand | ∀ {R : Type u} [inst : CommSemiring R] {p : ℕ}, 0 < p → ∀ {f : Polynomial R}, (Polynomial.expand R p) f = 0 ↔ f = 0 | true |
MeasureTheory.measureReal_univ_pos | Mathlib.MeasureTheory.Measure.Real | ∀ {α : Type u_1} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ] [NeZero μ],
0 < μ.real Set.univ | true |
LieModuleHom.codRestrict.congr_simp | Mathlib.Algebra.Lie.Weights.Cartan | ∀ {R : Type u} {L : Type v} {M : Type w} {N : Type w₁} [inst : CommRing R] [inst_1 : LieRing L]
[inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : LieRingModule L M] [inst_5 : AddCommGroup N]
[inst_6 : Module R N] [inst_7 : LieRingModule L N] (P : LieSubmodule R L N) (f f_1 : M →ₗ⁅R,L⁆ N) (e_f : f = f_1)
(... | true |
List.SortedGT.reverse | Mathlib.Data.List.Sort | ∀ {α : Type u_1} {l : List α} [inst : Preorder α], l.SortedGT → l.reverse.SortedLT | true |
Std.ExtDTreeMap.Const.isSome_get?_iff_mem | 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]
{a : α}, (Std.ExtDTreeMap.Const.get? t a).isSome = true ↔ a ∈ t | true |
CategoryTheory.End.smul_left | Mathlib.CategoryTheory.Endomorphism | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {r : (CategoryTheory.End X)ᵐᵒᵖ} {f : X ⟶ Y},
r • f = CategoryTheory.CategoryStruct.comp (MulOpposite.unop r) f | true |
StarAddMonoid.mk | Mathlib.Algebra.Star.Basic | {R : Type u} →
[inst : AddMonoid R] →
[toInvolutiveStar : InvolutiveStar R] → (∀ (r s : R), star (r + s) = star r + star s) → StarAddMonoid R | true |
CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles._proof_6 | Mathlib.Algebra.Homology.ExactSequenceFour | ∀ {n : ℕ} (k : ℕ),
autoParam (k ≤ n) CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles._auto_1 → k + 1 + 2 ≤ n + 3 | false |
CategoryTheory.MonoOver.supLe._proof_1 | Mathlib.CategoryTheory.Subobject.Lattice | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [CategoryTheory.Limits.HasBinaryCoproducts C] {A : C}
(f g : CategoryTheory.MonoOver A), CategoryTheory.Limits.HasColimit (CategoryTheory.Limits.pair f.obj.left g.obj.left) | false |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_498 | Mathlib.CategoryTheory.ComposableArrows.Basic | Lean.Syntax | false |
Num.pos.injEq | Mathlib.Data.Num.Basic | ∀ (a a_1 : PosNum), (Num.pos a = Num.pos a_1) = (a = a_1) | true |
Function.FromTypes | Mathlib.Logic.Function.FromTypes | {n : ℕ} → (Fin n → Type u) → Type u → Type u | true |
_private.Lean.Server.FileWorker.ExampleHover.0.Lean.Server.FileWorker.Hover.RWState.output.injEq | Lean.Server.FileWorker.ExampleHover | ∀ (indent ticks indent_1 ticks_1 : ℕ),
(Lean.Server.FileWorker.Hover.RWState.output✝ indent ticks =
Lean.Server.FileWorker.Hover.RWState.output✝¹ indent_1 ticks_1) =
(indent = indent_1 ∧ ticks = ticks_1) | true |
Lean.Elab.Term.elabStateRefT | Lean.Elab.BuiltinNotation | Lean.Elab.Term.TermElab | true |
Real.instFloorRing | Mathlib.Data.Real.Archimedean | FloorRing ℝ | true |
Std.DTreeMap.Equiv.foldrM_eq | Std.Data.DTreeMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.DTreeMap α β cmp} {δ : Type w}
{m : Type w → Type w'} [Std.TransCmp cmp] [inst : Monad m] [LawfulMonad m] {f : (a : α) → β a → δ → m δ} {init : δ},
t₁.Equiv t₂ → Std.DTreeMap.foldrM f init t₁ = Std.DTreeMap.foldrM f init t₂ | true |
Subsemiring.mk'._proof_4 | Mathlib.Algebra.Ring.Subsemiring.Defs | ∀ {R : Type u_1} [inst : NonAssocSemiring R] (s : Set R) (sa : AddSubmonoid R), ↑sa = s → 0 ∈ s | false |
deriv_fun_pow | Mathlib.Analysis.Calculus.Deriv.Pow | ∀ {𝕜 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {f : 𝕜 → 𝔸} {x : 𝕜},
DifferentiableAt 𝕜 f x → ∀ (n : ℕ), deriv (fun x => f x ^ n) x = ↑n * f x ^ (n - 1) * deriv f x | true |
Int.Cooper.mul_resolve_left_inv_le | Init.Data.Int.Cooper | ∀ {b q : ℤ} (a p k : ℤ), 0 < a → b * k + b * p ≤ a * q → a ∣ k + p → b * Int.Cooper.resolve_left_inv a p k ≤ q | true |
CategoryTheory.ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj | Mathlib.CategoryTheory.Abelian.LeftDerived | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{D : Type u_1} →
[inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
[inst_2 : CategoryTheory.Abelian C] →
[inst_3 : CategoryTheory.HasProjectiveResolutions C] →
[inst_4 : CategoryTheory.Abelian D] →
{X : C}... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.mem_toList_iff_getKey?_eq_some_and_get?_eq_some._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) | false |
monotoneOn_univ._simp_1 | Mathlib.Order.Monotone.Defs | ∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β}, MonotoneOn f Set.univ = Monotone f | false |
CategoryTheory.Functor.IsDenseSubsite.sheafEquiv | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{D : Type u_2} →
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
(J : CategoryTheory.GrothendieckTopology C) →
(K : CategoryTheory.GrothendieckTopology D) →
(G : CategoryTheory.Functor C D) →
(A : ... | true |
Std.DHashMap.mem_toArray_iff_get?_eq_some | Std.Data.DHashMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.DHashMap α β} [inst : LawfulBEq α] {k : α}
{v : β k}, ⟨k, v⟩ ∈ m.toArray ↔ m.get? k = some v | true |
_private.Mathlib.Tactic.Linter.FlexibleLinter.0.Mathlib.Linter.Flexible.TacticData.mk.sizeOf_spec | Mathlib.Tactic.Linter.FlexibleLinter | ∀ (stx : Lean.Syntax) (ci : Lean.Elab.ContextInfo) (mctxBefore mctxAfter : Lean.MetavarContext)
(goalsTargetedBy goalsCreatedBy : List Lean.MVarId),
sizeOf
{ stx := stx, ci := ci, mctxBefore := mctxBefore, mctxAfter := mctxAfter, goalsTargetedBy := goalsTargetedBy,
goalsCreatedBy := goalsCreatedBy } =... | true |
smul_add_smul_le_smul_add_smul | Mathlib.Algebra.Order.Module.Defs | ∀ {α : Type u_1} {β : Type u_2} [inst : Semiring α] [inst_1 : PartialOrder α] [IsStrictOrderedRing α] [ExistsAddOfLE α]
[inst_4 : AddCommMonoid β] [inst_5 : PartialOrder β] [IsOrderedCancelAddMonoid β] [inst_7 : Module α β]
[PosSMulMono α β] {a₁ a₂ : α} {b₁ b₂ : β}, a₁ ≤ a₂ → b₁ ≤ b₂ → a₁ • b₂ + a₂ • b₁ ≤ a₁ • b₁ +... | true |
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