name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
List.toList_mkSlice_roc | Init.Data.Slice.List.Lemmas | ∀ {α : Type u_1} {xs : List α} {lo hi : ℕ},
Std.Slice.toList (Std.Roc.Sliceable.mkSlice xs lo<...=hi) = List.drop (lo + 1) (List.take (hi + 1) xs) | true |
_private.Lean.Util.OccursCheck.0.Lean.occursCheck.visit._unsafe_rec | Lean.Util.OccursCheck | {m : Type → Type} → [Monad m] → [Lean.MonadMCtx m] → Lean.MVarId → Lean.Expr → ExceptT Unit (StateT Lean.ExprSet m) Unit | false |
Array.pmap_ne_empty_iff | Init.Data.Array.Attach | ∀ {α : Type u_1} {β : Type u_2} {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α} (H : ∀ a ∈ xs, P a),
Array.pmap f xs H ≠ #[] ↔ xs ≠ #[] | true |
PointedCone.dual_le_dual | Mathlib.Geometry.Convex.Cone.Dual | ∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R] {M : Type u_2}
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] {N : Type u_3} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
{p : M →ₗ[R] N →ₗ[R] R} {s t : Set M}, t ⊆ s → PointedCone.dual p s ≤ PointedCone.dual p t | true |
Std.ExtTreeMap.minKey!_insertIfNew_le_self | Std.Data.ExtTreeMap.Lemmas | ∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp]
[inst_1 : Inhabited α] {k : α} {v : β}, (cmp (t.insertIfNew k v).minKey! k).isLE = true | true |
TensorProduct.instInhabited | Mathlib.LinearAlgebra.TensorProduct.Defs | {R : Type u_1} →
[inst : CommSemiring R] →
(M : Type u_7) →
(N : Type u_8) →
[inst_1 : AddCommMonoid M] →
[inst_2 : AddCommMonoid N] → [inst_3 : Module R M] → [inst_4 : Module R N] → Inhabited (TensorProduct R M N) | true |
MulRingNorm._sizeOf_1 | Mathlib.Analysis.Normed.Unbundled.RingSeminorm | {R : Type u_2} → {inst : NonAssocRing R} → [SizeOf R] → MulRingNorm R → ℕ | false |
Aesop.Index.mk.inj | Aesop.Index | ∀ {α : Type} {byTarget byHyp : Lean.Meta.DiscrTree (Aesop.Rule α)} {unindexed : Lean.PHashSet (Aesop.Rule α)}
{byTarget_1 byHyp_1 : Lean.Meta.DiscrTree (Aesop.Rule α)} {unindexed_1 : Lean.PHashSet (Aesop.Rule α)},
{ byTarget := byTarget, byHyp := byHyp, unindexed := unindexed } =
{ byTarget := byTarget_1, byH... | true |
Nat.digits_ne_nil_iff_ne_zero | Mathlib.Data.Nat.Digits.Defs | ∀ {b n : ℕ}, b.digits n ≠ [] ↔ n ≠ 0 | true |
ContinuousLinearMap.opNorm_add_le | Mathlib.Analysis.Normed.Operator.Basic | ∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : SeminormedAddCommGroup E]
[inst_1 : SeminormedAddCommGroup F] [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜₂]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂] (f g ... | true |
Finset.nsmul_right_monotone | Mathlib.Algebra.Group.Pointwise.Finset.Basic | ∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : AddMonoid α] {s : Finset α}, 0 ∈ s → Monotone fun x => x • s | true |
IsLocalMin.add | Mathlib.Topology.Order.LocalExtr | ∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : AddCommMonoid β] [inst_2 : PartialOrder β]
[IsOrderedAddMonoid β] {f g : α → β} {a : α}, IsLocalMin f a → IsLocalMin g a → IsLocalMin (fun x => f x + g x) a | true |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.option.match_5 | Lean.Elab.DocString.Builtin | (motive : Lean.Syntax ⊕ Lean.Syntax → Sort u_1) →
(spec : Lean.Syntax ⊕ Lean.Syntax) →
((stx : Lean.Syntax) → motive (Sum.inl stx)) → ((stx : Lean.Syntax) → motive (Sum.inr stx)) → motive spec | false |
Aesop.Script.TacticBuilder.simpAllOrSimpAtStarOnly | Aesop.Script.SpecificTactics | Bool → Lean.MVarId → Option Lean.Term → Lean.Meta.Simp.UsedSimps → Aesop.Script.TacticBuilder | true |
LLVM.parseBitcode | Lean.Compiler.IR.LLVMBindings | (ctx : LLVM.Context) → LLVM.MemoryBuffer ctx → BaseIO (LLVM.Module ctx) | true |
LinearMap.detAux.congr_simp | Mathlib.LinearAlgebra.Determinant | ∀ {M : Type u_7} [inst : AddCommGroup M] {ι : Type u_8} {inst_1 : DecidableEq ι} [inst_2 : DecidableEq ι]
[inst_3 : Fintype ι] {A : Type u_9} [inst_4 : CommRing A] [inst_5 : Module A M] (a a_1 : Trunc (Module.Basis ι A M)),
a = a_1 → LinearMap.detAux a = LinearMap.detAux a_1 | true |
OrderHom.le_prevFixed_iff._simp_1 | Mathlib.Order.FixedPoints | ∀ {α : Type u} [inst : CompleteLattice α] (f : α →o α) {x : α} (hx : f x ≤ x) {y : ↑(Function.fixedPoints ⇑f)},
(y ≤ f.prevFixed x hx) = (↑y ≤ x) | false |
CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem._proof_2 | Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | ∀ {J : Type u_1} [inst : LinearOrder J] {j : J} {i₁ : ↑(Set.Iio j)}, (fun a => ↑a) i₁ ≤ ↑i₁ | false |
cmp_sub_zero | Mathlib.Algebra.Order.Group.Unbundled.Basic | ∀ {α : Type u} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddRightMono α] (a b : α), cmp (a - b) 0 = cmp a b | true |
CategoryTheory.Pseudofunctor.DescentData'._sizeOf_1 | Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime | {C : Type u} →
{inst : CategoryTheory.Category.{v, u} C} →
{F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ) CategoryTheory.Cat} →
{ι : Type t} →
{S : C} →
{X : ι → C} →
{f : (i : ι) → X i ⟶ S} →
{sq : (i j : ι) → CategoryTheory.Limits.ChosenP... | false |
Module.ker_algebraMap_end | Mathlib.Algebra.Algebra.Basic | ∀ (K : Type u) (V : Type v) [inst : Semifield K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V] (a : K),
a ≠ 0 → LinearMap.ker ((algebraMap K (Module.End K V)) a) = ⊥ | true |
_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxc.Iterator.instIteratorLoop.loop.match_3.eq_1 | Init.Data.Range.Polymorphic.RangeIterator | ∀ {α : Type u_1} (γ : Type u_1) (Pl : α → γ → ForInStep γ → Prop) (next : α) (acc : γ)
(motive : Subtype (Pl next acc) → Sort u_2) (acc' : γ) (h' : Pl next acc (ForInStep.yield acc'))
(h_1 : (acc' : γ) → (h' : Pl next acc (ForInStep.yield acc')) → motive ⟨ForInStep.yield acc', h'⟩)
(h_2 : (acc' : γ) → (property :... | true |
LSeries_neg | Mathlib.NumberTheory.LSeries.Linearity | ∀ (f : ℕ → ℂ) (s : ℂ), LSeries (-f) s = -LSeries f s | true |
BoolAlg.dual | Mathlib.Order.Category.BoolAlg | CategoryTheory.Functor BoolAlg BoolAlg | true |
_private.Mathlib.Topology.Instances.ENNReal.Lemmas.0.tendsto_iff_edist_tendsto_0._simp_1_1 | Mathlib.Topology.Instances.ENNReal.Lemmas | ∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {ε : ENNReal}, (y ∈ Metric.eball x ε) = (edist y x < ε) | false |
Lean.Meta.Grind.Arith.CommRing.State | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | Type | true |
Array.attachWith_map.match_1 | Init.Data.Array.Attach | {α : Type u_1} →
{β : Type u_2} →
{f : α → β} →
{P : β → Prop} →
(motive : { x // (P ∘ f) x } → Sort u_3) →
(x : { x // (P ∘ f) x }) → ((x : α) → (h : (P ∘ f) x) → motive ⟨x, h⟩) → motive x | false |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalFunCases | Lean.Elab.Tactic.Induction | Lean.Elab.Tactic.Tactic | true |
_private.Init.Data.String.Lemmas.Pattern.Char.0.String.Slice.Pattern.Model.Char.instLawfulForwardPatternModelChar.match_2 | Init.Data.String.Lemmas.Pattern.Char | ∀ {c : Char} {s : String.Slice} (pos : s.Pos)
(motive : (∃ (h : ¬s.startPos = s.endPos), s.startPos.get ⋯ = c ∧ s.startPos.next ⋯ = pos) → Prop)
(x : ∃ (h : ¬s.startPos = s.endPos), s.startPos.get ⋯ = c ∧ s.startPos.next ⋯ = pos),
(∀ (h : ¬s.startPos = s.endPos) (h₁ : s.startPos.get ⋯ = c) (h₂ : s.startPos.next ⋯... | false |
Lean.PrettyPrinter.Delaborator.delabStructureInstance._regBuiltin.Lean.PrettyPrinter.Delaborator.delabStructureInstance_1 | Lean.PrettyPrinter.Delaborator.Builtins | IO Unit | false |
OrderDual.instIsLowerSet | Mathlib.Topology.Order.UpperLowerSetTopology | ∀ {α : Type u_1} [inst : Preorder α] [inst_1 : TopologicalSpace α] [Topology.IsUpperSet α], Topology.IsLowerSet αᵒᵈ | true |
Std.DTreeMap.Internal.Impl.maxEntry! | Std.Data.DTreeMap.Internal.Queries | {α : Type u} → {β : α → Type v} → [Inhabited ((a : α) × β a)] → Std.DTreeMap.Internal.Impl α β → (a : α) × β a | true |
ContDiffOn.div_const | Mathlib.Analysis.Calculus.ContDiff.Operations | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {s : Set E} {𝕜' : Type u_6} [inst_3 : NormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
{f : E → 𝕜'} {n : WithTop ℕ∞}, ContDiffOn 𝕜 n f s → ∀ (c : 𝕜'), ContDiffOn 𝕜 n (fun x => f x / c... | true |
CategoryTheory.ShortComplex.QuasiIso.mk | Mathlib.Algebra.Homology.ShortComplex.QuasiIso | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology] {φ : S₁ ⟶ S₂},
CategoryTheory.IsIso (CategoryTheory.ShortComplex.homologyMap φ) → CategoryTheory.ShortComplex... | true |
Fin.findSome?_eq_findSome?_finRange | Batteries.Data.Fin.Lemmas | ∀ {n : ℕ} {α : Type u_1} (f : Fin n → Option α), Fin.findSome? f = List.findSome? f (List.finRange n) | true |
_private.Mathlib.Tactic.Linarith.Preprocessing.0.Mathlib.Tactic.Linarith.splitConjunctions.aux._sparseCasesOn_1 | Mathlib.Tactic.Linarith.Preprocessing | {motive : Lean.Name → Sort u} →
(t : Lean.Name) →
((pre : Lean.Name) → (str : String) → motive (pre.str str)) → (Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t | false |
CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCycles_assoc | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C} (h : S.LeftHomologyData) [inst_2 : S.HasLeftHomology] {Z : C} (h_1 : S.X₂ ⟶ Z),
CategoryTheory.CategoryStruct.comp h.cyclesIso.inv (CategoryTheory.CategoryStruct.com... | true |
Std.CancellationReason.cancel.elim | Std.Sync.CancellationToken | {motive : Std.CancellationReason → Sort u} →
(t : Std.CancellationReason) → t.ctorIdx = 2 → motive Std.CancellationReason.cancel → motive t | false |
FirstOrder.Language.ElementarilyEquivalent | Mathlib.ModelTheory.Semantics | (L : FirstOrder.Language) → (M : Type w) → (N : Type u_1) → [L.Structure M] → [L.Structure N] → Prop | true |
Lean.Compiler.LCNF.LCtx.mk | Lean.Compiler.LCNF.LCtx | Std.HashMap Lean.FVarId (Lean.Compiler.LCNF.Param Lean.Compiler.LCNF.Purity.pure) →
Std.HashMap Lean.FVarId (Lean.Compiler.LCNF.Param Lean.Compiler.LCNF.Purity.impure) →
Std.HashMap Lean.FVarId (Lean.Compiler.LCNF.LetDecl Lean.Compiler.LCNF.Purity.pure) →
Std.HashMap Lean.FVarId (Lean.Compiler.LCNF.LetDecl ... | true |
MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop | Mathlib.MeasureTheory.Measure.Haar.Unique | ∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [inst_2 : IsTopologicalAddGroup G]
[inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] [LocallyCompactSpace G] (μ' μ : MeasureTheory.Measure G)
[inst_6 : μ.IsAddHaarMeasure] [inst_7 : MeasureTheory.IsFiniteMeasureOnCompacts μ'] [inst_8 : μ'.IsAddLe... | true |
Polynomial.mem_degreeLT | Mathlib.RingTheory.Polynomial.Basic | ∀ {R : Type u} [inst : Semiring R] {n : ℕ} {f : Polynomial R}, f ∈ Polynomial.degreeLT R n ↔ f.degree < ↑n | true |
CategoryTheory.MonoidalCategory.prodMonoidal.match_1 | Mathlib.CategoryTheory.Monoidal.Category | (C₁ : Type u_1) →
(C₂ : Type u_2) → (motive : C₁ × C₂ → Sort u_3) → (x : C₁ × C₂) → ((X₁ : C₁) → (X₂ : C₂) → motive (X₁, X₂)) → motive x | false |
Set.ncard_image_le._auto_1 | Mathlib.Data.Set.Card | Lean.Syntax | false |
Std.DHashMap.Internal.Raw₀.interSmallerFn | Std.Data.DHashMap.Internal.Defs | {α : Type u} →
{β : α → Type v} →
[BEq α] →
[Hashable α] →
Std.DHashMap.Internal.Raw₀ α β → Std.DHashMap.Internal.Raw₀ α β → α → Std.DHashMap.Internal.Raw₀ α β | true |
Lean.Lsp.CompletionItem._sizeOf_1 | Lean.Data.Lsp.LanguageFeatures | Lean.Lsp.CompletionItem → ℕ | false |
ZeroHom.recOn | Mathlib.Algebra.Group.Hom.Defs | {M : Type u_10} →
{N : Type u_11} →
[inst : Zero M] →
[inst_1 : Zero N] →
{motive : ZeroHom M N → Sort u} →
(t : ZeroHom M N) →
((toFun : M → N) → (map_zero' : toFun 0 = 0) → motive { toFun := toFun, map_zero' := map_zero' }) → motive t | false |
Antitone.tendstoLocallyUniformly_of_forall_tendsto | Mathlib.Topology.UniformSpace.Dini | ∀ {ι : Type u_1} {α : Type u_2} {G : Type u_3} [inst : Preorder ι] [inst_1 : TopologicalSpace α]
[inst_2 : NormedAddCommGroup G] [inst_3 : Lattice G] [HasSolidNorm G] [IsOrderedAddMonoid G] {F : ι → α → G}
{f : α → G},
(∀ (i : ι), Continuous (F i)) →
Antitone F →
Continuous f →
(∀ (x : α), Filte... | true |
Measurable.fst | Mathlib.MeasureTheory.MeasurableSpace.Constructions | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {m : MeasurableSpace α} {mβ : MeasurableSpace β} {mγ : MeasurableSpace γ}
{f : α → β × γ}, Measurable f → Measurable fun a => (f a).1 | true |
Language.reverse_add | Mathlib.Computability.Language | ∀ {α : Type u_1} (l m : Language α), (l + m).reverse = l.reverse + m.reverse | true |
Lean.Server.References.recOn | Lean.Server.References | {motive : Lean.Server.References → Sort u} →
(t : Lean.Server.References) →
((ileans : Lean.Server.ILeanMap) →
(workers : Lean.Server.WorkerRefMap) → motive { ileans := ileans, workers := workers }) →
motive t | false |
Std.Rxc.Iterator.Monadic.isPlausibleIndirectOutput_iff | Init.Data.Range.Polymorphic.RangeIterator | ∀ {α : Type u} [inst : Std.PRange.UpwardEnumerable α] [inst_1 : LE α] [inst_2 : DecidableLE α]
[Std.PRange.LawfulUpwardEnumerableLE α] [Std.PRange.LawfulUpwardEnumerable α] {it : Std.IterM Id α} {out : α},
it.IsPlausibleIndirectOutput out ↔
∃ n, (it.internalState.next.bind fun x => Std.PRange.succMany? n x) = s... | true |
Finsupp.restrictSupportEquiv._proof_2 | Mathlib.Data.Finsupp.Basic | ∀ {α : Type u_1} (s : Set α) (M : Type u_2) [inst : AddCommMonoid M] (f : { f // ↑f.support ⊆ s }),
↑(Finsupp.subtypeDomain (fun x => x ∈ s) ↑f).extendDomain.support ⊆ {x | x ∈ s} | false |
ContDiffMapSupportedIn.noConfusion | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | {P : Sort u} →
{E : Type u_2} →
{F : Type u_3} →
{inst : NormedAddCommGroup E} →
{inst_1 : NormedSpace ℝ E} →
{inst_2 : NormedAddCommGroup F} →
{inst_3 : NormedSpace ℝ F} →
{n : ℕ∞} →
{K : TopologicalSpace.Compacts E} →
{t : ContD... | false |
CharP.ringChar_ne_one | Mathlib.Algebra.CharP.Defs | ∀ {R : Type u_1} [inst : NonAssocSemiring R] [Nontrivial R], ringChar R ≠ 1 | true |
CochainComplex.HomComplex.Cocycle.toSingleMk_coe | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] {X : C} {K : CochainComplex C ℤ} {p q : ℤ} (f : K.X p ⟶ X) {n : ℤ}
(h : p + n = q) (p' : ℤ) (hp' : p' + 1 = p) (hf : CategoryTheory.CategoryStruct.comp (K.d p' p) f = 0),... | true |
TensorProduct.instNormedAddCommGroup._proof_6 | Mathlib.Analysis.InnerProductSpace.TensorProduct | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F]
(x y : TensorProduct 𝕜 E F), (starRingEnd 𝕜) (inner 𝕜 y x) = inner 𝕜 x y | false |
CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u} [inst_1 : CategoryTheory.Category.{v, u} D]
{x y : C} (f : x ⟶ y) (F : CategoryTheory.Functor C D),
CategoryTheory.nerve.homEquiv ((CategoryTheory.nerve.edgeMk f).map (CategoryTheory.nerveMap F)) = F.map f | true |
Std.Iterators.Types.Zip.instFinitenessRelation₁ | Std.Data.Iterators.Combinators.Monadic.Zip | {m : Type w → Type w'} →
{α₁ β₁ : Type w} →
[inst : Std.Iterator α₁ m β₁] →
{α₂ β₂ : Type w} →
[inst_1 : Std.Iterator α₂ m β₂] →
[inst_2 : Monad m] →
[Std.Iterators.Finite α₁ m] →
[Std.Iterators.Productive α₂ m] → Std.Iterators.FinitenessRelation (Std.Iterators.Ty... | true |
QuadraticModuleCat.forget₂_map_associator_inv | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal | ∀ {R : Type u} [inst : CommRing R] [inst_1 : Invertible 2] (X Y Z : QuadraticModuleCat R),
(CategoryTheory.forget₂ (QuadraticModuleCat R) (ModuleCat R)).map
(CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv =
(CategoryTheory.MonoidalCategoryStruct.associator X.toModuleCat Y.toModuleCat Z.toModule... | true |
_private.Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure.0.AlgebraicClosure.isAlgebraic.match_1 | Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure | ∀ (k : Type u_1) [inst : Field k] (z : AlgebraicClosure k)
(motive : (∃ a, (Ideal.Quotient.mk (AlgebraicClosure.maxIdeal k)) a = z) → Prop)
(x : ∃ a, (Ideal.Quotient.mk (AlgebraicClosure.maxIdeal k)) a = z),
(∀ (p : MvPolynomial (AlgebraicClosure.Vars k) k) (hp : (Ideal.Quotient.mk (AlgebraicClosure.maxIdeal k)) ... | false |
BitVec.reduceEq | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | Lean.Meta.Simp.Simproc | true |
«_aux_ImportGraph_Tools_ImportDiff___elabRules_command#import_diff__1» | ImportGraph.Tools.ImportDiff | Lean.Elab.Command.CommandElab | false |
Complex.norm_exp_ofReal_mul_I | Mathlib.Analysis.Complex.Trigonometric | ∀ (x : ℝ), ‖Complex.exp (↑x * Complex.I)‖ = 1 | true |
EuclideanGeometry.Concyclic.subset | Mathlib.Geometry.Euclidean.Sphere.Basic | ∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {ps₁ ps₂ : Set P},
ps₁ ⊆ ps₂ → EuclideanGeometry.Concyclic ps₂ → EuclideanGeometry.Concyclic ps₁ | true |
Nat.toArray_roc_add_succ_right_eq_push | Init.Data.Range.Polymorphic.NatLemmas | ∀ {m n : ℕ}, (m<...=m + n + 1).toArray = (m<...=m + n).toArray.push (m + n + 1) | true |
Subfield.map_le_iff_le_comap | Mathlib.Algebra.Field.Subfield.Basic | ∀ {K : Type u} {L : Type v} [inst : DivisionRing K] [inst_1 : DivisionRing L] {f : K →+* L} {s : Subfield K}
{t : Subfield L}, Subfield.map f s ≤ t ↔ s ≤ Subfield.comap f t | true |
Complex.re_le_norm | Mathlib.Analysis.Complex.Norm | ∀ (z : ℂ), z.re ≤ ‖z‖ | true |
Lean.Meta.Simp.isBuiltinSimproc | Lean.Meta.Tactic.Simp.Simproc | Lean.Name → Lean.CoreM Bool | true |
_private.Mathlib.Data.FinEnum.Option.0.FinEnum.recEmptyOption.match_1.eq_1 | Mathlib.Data.FinEnum.Option | ∀ (motive : ℕ → Sort u_1) (h_1 : 0 = 0 → motive 0) (h_2 : (n : ℕ) → 0 = n.succ → motive n.succ),
(match cardeq : 0 with
| 0 => h_1 cardeq
| n.succ => h_2 n cardeq) =
h_1 ⋯ | true |
CategoryTheory.Limits.imageSubobject_iso_comp | Mathlib.CategoryTheory.Subobject.Limits | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [CategoryTheory.Limits.HasEqualizers C] {X' : C}
(h : X' ⟶ X) [inst_2 : CategoryTheory.IsIso h] (f : X ⟶ Y) [inst_3 : CategoryTheory.Limits.HasImage f],
CategoryTheory.Limits.imageSubobject (CategoryTheory.CategoryStruct.comp h f) = CategoryTheory.L... | true |
NonUnitalSubring.mk._flat_ctor | Mathlib.RingTheory.NonUnitalSubring.Defs | {R : Type u} →
[inst : NonUnitalNonAssocRing R] →
(carrier : Set R) →
(∀ {a b : R}, a ∈ carrier → b ∈ carrier → a + b ∈ carrier) →
0 ∈ carrier →
(∀ {a b : R}, a ∈ carrier → b ∈ carrier → a * b ∈ carrier) →
(∀ {x : R}, x ∈ carrier → -x ∈ carrier) → NonUnitalSubring R | false |
_private.Mathlib.Topology.UniformSpace.UniformConvergence.0.tendstoUniformlyOn_iff_tendstoUniformlyOnFilter._simp_1_3 | Mathlib.Topology.UniformSpace.UniformConvergence | ∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {p : α × β → Prop} {s : Set β},
(∀ᶠ (x : α × β) in f ×ˢ Filter.principal s, p x) = ∀ᶠ (x : α) in f, ∀ y ∈ s, p (x, y) | false |
ContMDiffMap.coeFnMonoidHom.eq_1 | Mathlib.Geometry.Manifold.Algebra.SmoothFunctions | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_4}
[inst_5 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {H' : Type u_5} [inst_6 : Topologi... | true |
Set.forall_subset_range_iff._simp_1 | Mathlib.Data.Set.Image | ∀ {α : Type u_1} {β : Type u_2} {f : α → β} {p : Set β → Prop}, (∀ s ⊆ Set.range f, p s) = ∀ (s : Set α), p (f '' s) | false |
CategoryTheory.ExponentiableMorphism.OverMkHom | Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{I J : C} →
{f : I ⟶ J} →
[inst_1 : CategoryTheory.ChosenPullbacksAlong f] →
[CategoryTheory.ExponentiableMorphism f] → CategoryTheory.ExponentiableMorphism (CategoryTheory.Over.mk f).hom | true |
AlgebraicGeometry.Scheme.Pullback.openCoverOfBase'._proof_2 | Mathlib.AlgebraicGeometry.Pullbacks | ∀ {X Y Z : AlgebraicGeometry.Scheme} (𝒰 : Z.OpenCover) (f : X ⟶ Z) (g : Y ⟶ Z)
(i :
(AlgebraicGeometry.Scheme.Pullback.openCoverOfLeft (CategoryTheory.Precoverage.ZeroHypercover.pullback₁ f 𝒰) f
g).I₀),
CategoryTheory.Limits.HasPullback f (𝒰.f i) | false |
MeasureTheory.lintegral_add_mul_meas_add_le_le_lintegral | Mathlib.MeasureTheory.Integral.Lebesgue.Markov | ∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
f ≤ᵐ[μ] g → AEMeasurable g μ → ∀ (ε : ENNReal), ∫⁻ (a : α), f a ∂μ + ε * μ {x | f x + ε ≤ g x} ≤ ∫⁻ (a : α), g a ∂μ | true |
Aesop.Hyp | Aesop.Forward.State | Type | true |
Lean.LocalDecl.setNondep | Lean.LocalContext | Lean.LocalDecl → Bool → Lean.LocalDecl | true |
Lean.Compiler.LCNF.UnreachableBranches.Value.ctorElimType | Lean.Compiler.LCNF.ElimDeadBranches | {motive_1 : Lean.Compiler.LCNF.UnreachableBranches.Value → Sort u} → ℕ → Sort (max 1 u) | false |
Lean.Parser.Term.unreachable._regBuiltin.Lean.Parser.Term.unreachable_1 | Lean.Parser.Term | IO Unit | false |
Lean.Elab.InfoTree.context.elim | Lean.Elab.InfoTree.Types | {motive_1 : Lean.Elab.InfoTree → Sort u} →
(t : Lean.Elab.InfoTree) →
t.ctorIdx = 0 →
((i : Lean.Elab.PartialContextInfo) → (t : Lean.Elab.InfoTree) → motive_1 (Lean.Elab.InfoTree.context i t)) →
motive_1 t | false |
Lean.Compiler.LCNF.Simp.Config.noConfusionType | Lean.Compiler.LCNF.Simp.Config | Sort u → Lean.Compiler.LCNF.Simp.Config → Lean.Compiler.LCNF.Simp.Config → Sort u | false |
ThreeGPFree.prod | Mathlib.Combinatorics.Additive.AP.Three.Defs | ∀ {α : Type u_2} {β : Type u_3} [inst : Monoid α] [inst_1 : Monoid β] {s : Set α} {t : Set β},
ThreeGPFree s → ThreeGPFree t → ThreeGPFree (s ×ˢ t) | true |
NNReal.instLinearOrder._aux_4 | Mathlib.Data.NNReal.Defs | DecidableLE NNReal | false |
contMDiffWithinAt_of_notMem_mulTSupport | Mathlib.Geometry.Manifold.ContMDiff.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] {E' : Type u_5} [inst_5 : NormedAddCommGroup E'] [inst_6 : NormedSp... | true |
Bool.beq_eq_decide_eq | Init.Data.Bool | ∀ {α : Type u_1} [inst : BEq α] [LawfulBEq α] [inst_2 : DecidableEq α] (a b : α), (a == b) = decide (a = b) | true |
Lean.NameGenerator.noConfusionType | Init.MetaTypes | Sort u → Lean.NameGenerator → Lean.NameGenerator → Sort u | false |
MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv | Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
[FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (f : E ≃L[ℝ] E) (s : Set E),
μ (⇑f ⁻¹' s) = ENNReal.ofReal |LinearMap.det ↑↑f.symm| * μ s | true |
Lists.Equiv.decidable._mutual._proof_4 | Mathlib.SetTheory.Lists | ∀ {α : Type u_1} (b : Bool) (a : Lists' α b) (l₁ l₂ : Lists' α true),
sizeOf ⟨b, a⟩ < 1 + 1 + sizeOf a + sizeOf l₁ →
InvImage (fun x1 x2 => x1 < x2)
(fun x =>
PSum.casesOn x (fun _x => PSigma.casesOn _x fun l₁ l₂ => sizeOf l₁ + sizeOf l₂) fun _x =>
PSum.casesOn _x (fun _x => PSigma.casesOn... | false |
Finpartition.sparsePairs_mono | Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | ∀ {α : Type u_1} {𝕜 : Type u_2} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : DecidableEq α] {A : Finset α}
(P : Finpartition A) (G : SimpleGraph α) [inst_3 : DecidableRel G.Adj] {ε ε' : 𝕜},
ε ≤ ε' → P.sparsePairs G ε ⊆ P.sparsePairs G ε' | true |
Std.DHashMap.Const.mem_alter | 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] {k k' : α} {f : Option β → Option β},
k' ∈ Std.DHashMap.Const.alter m k f ↔
if (k == k') = true then (f (Std.DHashMap.Const.get? m k)).isSome = true else k' ∈ m | true |
ApproximatesLinearOn.toHomeomorph._proof_3 | Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | ∀ {𝕜 : Type u_3} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_1} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E → F)
{f' : E ≃L[𝕜] F} {c : NNReal} [inst_5 : CompleteSpace E] (hf : ApproximatesLinearOn f (↑f') Set.uni... | false |
Lean.Expr.binderInfoEx | Lean.Expr | Lean.Expr → Lean.BinderInfo | true |
CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.transfiniteCompositionOfShapeMapFromBot | Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{G : C} →
[inst_1 : CategoryTheory.Abelian C] →
(hG : CategoryTheory.IsSeparator G) →
{X : C} →
[inst_2 : CategoryTheory.IsGrothendieckAbelian.{w, v, u} C] →
(A₀ : CategoryTheory.Subobject X) →
... | true |
covBy_sup_of_inf_covBy_of_inf_covBy_left | Mathlib.Order.ModularLattice | ∀ {α : Type u_1} [inst : Lattice α] [IsWeakUpperModularLattice α] {a b : α}, a ⊓ b ⋖ a → a ⊓ b ⋖ b → a ⋖ a ⊔ b | true |
CategoryTheory.StructuredArrow.subobjectEquiv._proof_2 | Mathlib.CategoryTheory.Subobject.Comma | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {D : Type u_4}
[inst_1 : CategoryTheory.Category.{u_3, u_4} D] {S : D} {T : CategoryTheory.Functor C D}
[inst_2 : CategoryTheory.Limits.HasFiniteLimits C] [inst_3 : CategoryTheory.Limits.PreservesFiniteLimits T]
(A : CategoryTheory.StructuredArrow S T... | false |
LinearMap.rTensor_tmul | Mathlib.LinearAlgebra.TensorProduct.Map | ∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
[inst_6 : Module R P] (f : N →ₗ[R] P) (m : M) (n : N), (LinearMap.rTensor M f) (n ⊗ₜ[R] m) = f n ⊗ₜ[R] m | true |
strictAnti_of_hasDerivAt_neg | Mathlib.Analysis.Calculus.Deriv.MeanValue | ∀ {f f' : ℝ → ℝ}, (∀ (x : ℝ), HasDerivAt f (f' x) x) → (∀ (x : ℝ), f' x < 0) → StrictAnti f | true |
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