name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
ArchimedeanClass.mk_nonneg_of_le_of_le_of_archimedean | Mathlib.Algebra.Order.Ring.Archimedean | ∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : CommRing R] [inst_2 : IsStrictOrderedRing R] {S : Type u_3}
[inst_3 : LinearOrder S] [inst_4 : CommRing S] [IsStrictOrderedRing S] [Archimedean S] (f : S →+*o R) {x : R}
{r s : S}, f r ≤ x → x ≤ f s → 0 ≤ ArchimedeanClass.mk x | true |
CommRingCat.Colimits.instCommRingColimitType._proof_9 | Mathlib.Algebra.Category.Ring.Colimits | ∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J CommRingCat)
(x : CommRingCat.Colimits.ColimitType F), 0 * x = 0 | false |
Quaternion.imJ_star | Mathlib.Algebra.Quaternion | ∀ {R : Type u_3} [inst : CommRing R] (a : Quaternion R), (star a).imJ = -a.imJ | true |
List.splitAtD.go._sunfold | Batteries.Data.List.Basic | {α : Type u_1} → α → ℕ → List α → List α → List α × List α | false |
Lean.Meta.LazyDiscrTree.recOn | Lean.Meta.LazyDiscrTree | {α : Type} →
{motive : Lean.Meta.LazyDiscrTree α → Sort u} →
(t : Lean.Meta.LazyDiscrTree α) →
((tries : Array (Lean.Meta.LazyDiscrTree.Trie α)) →
(roots : Std.HashMap Lean.Meta.LazyDiscrTree.Key Lean.Meta.LazyDiscrTree.TrieIndex) →
motive { tries := tries, roots := roots }) →
... | false |
Mathlib.Tactic.Ring.ringCleanupRef | Mathlib.Tactic.Ring.Basic | IO.Ref (Lean.Expr → Lean.MetaM Lean.Expr) | true |
VitaliFamily.FineSubfamilyOn.index | Mathlib.MeasureTheory.Covering.VitaliFamily | {X : Type u_1} →
[inst : PseudoMetricSpace X] →
{m0 : MeasurableSpace X} →
{μ : MeasureTheory.Measure X} →
{v : VitaliFamily μ} → {f : X → Set (Set X)} → {s : Set X} → v.FineSubfamilyOn f s → Set (X × Set X) | true |
SimpleGraph.Walk.IsHamiltonian.fintype._proof_1 | Mathlib.Combinatorics.SimpleGraph.Hamiltonian | ∀ {α : Type u_1} [inst : DecidableEq α] {G : SimpleGraph α} {a b : α} {p : G.Walk a b},
p.IsHamiltonian → ∀ (x : α), x ∈ p.support.toFinset | false |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.suggestName.match_4 | Lean.Elab.DocString.Builtin | (motive : Lean.Exception → Sort u_1) → (x : Lean.Exception) → ((x : Lean.Exception) → motive x) → motive x | false |
Nat.odd_sub._simp_1 | Mathlib.Algebra.Ring.Parity | ∀ {m n : ℕ}, n ≤ m → Odd (m - n) = (Odd m ↔ Even n) | false |
CategoryTheory.Functor.elementsFunctor_map | Mathlib.CategoryTheory.Elements | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : CategoryTheory.Functor C (Type w)} (n : X ⟶ Y),
CategoryTheory.Functor.elementsFunctor.map n = (CategoryTheory.NatTrans.mapElements n).toCatHom | true |
WithZeroMulInt.toNNReal_le_one_iff | Mathlib.Data.Int.WithZero | ∀ {e : NNReal} {m : WithZero (Multiplicative ℤ)} (he : 1 < e), (WithZeroMulInt.toNNReal ⋯) m ≤ 1 ↔ m ≤ 1 | true |
Algebra.transcendental_ringHom_iff_of_comp_eq | Mathlib.RingTheory.Algebraic.Basic | ∀ {R : Type u} {S : Type u_1} {A : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
[inst_3 : Algebra R A] {B : Type u_2} [inst_4 : Ring B] [inst_5 : Algebra S B] {FRS : Type u_3} {FAB : Type u_4}
[inst_6 : EquivLike FRS R S] [inst_7 : RingEquivClass FRS R S] [inst_8 : EquivLike FAB A B]
[inst_... | true |
padicValRat.of_int | Mathlib.NumberTheory.Padics.PadicVal.Basic | ∀ {p : ℕ} {z : ℤ}, padicValRat p ↑z = ↑(padicValInt p z) | true |
orderBornology_isBounded._simp_1 | Mathlib.Topology.Order.Bornology | ∀ {α : Type u_1} {s : Set α} [inst : Lattice α] [inst_1 : Nonempty α], Bornology.IsBounded s = (BddBelow s ∧ BddAbove s) | false |
Std.Tactic.BVDecide.LRAT.Internal.Formula.rupAdd_sound | Std.Tactic.BVDecide.LRAT.Internal.Formula.Class | ∀ {α : outParam (Type u)} {β : outParam (Type v)} {inst : Std.Tactic.BVDecide.LRAT.Internal.Clause α β} {σ : Type w}
{inst_1 : Std.Tactic.BVDecide.LRAT.Internal.Entails α σ} [self : Std.Tactic.BVDecide.LRAT.Internal.Formula α β σ]
(f : σ) (c : β) (rupHints : Array ℕ) (f' : σ),
Std.Tactic.BVDecide.LRAT.Internal.Fo... | true |
CategoryTheory.Precoherent.recOn | Mathlib.CategoryTheory.Sites.Coherent.Basic | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{motive : CategoryTheory.Precoherent C → Sort u} →
(t : CategoryTheory.Precoherent C) →
((pullback :
∀ {B₁ B₂ : C} (f : B₂ ⟶ B₁) (α : Type) [Finite α] (X₁ : α → C) (π₁ : (a : α) → X₁ a ⟶ B₁),
CategoryTheor... | false |
max_mul_mul_left | Mathlib.Algebra.Order.Monoid.Unbundled.MinMax | ∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : Mul α] [MulLeftMono α] (a b c : α), max (a * b) (a * c) = a * max b c | true |
ProbabilityTheory.Kernel.ae_compProd_iff | Mathlib.Probability.Kernel.Composition.CompProd | ∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mγ : MeasurableSpace γ} {κ : ProbabilityTheory.Kernel α β} [ProbabilityTheory.IsSFiniteKernel κ]
{η : ProbabilityTheory.Kernel (α × β) γ} [ProbabilityTheory.IsSFiniteKernel η] {a : α} {p : β × γ → Prop},
MeasurableSe... | true |
Equiv.forall_congr' | Mathlib.Logic.Equiv.Defs | ∀ {α : Sort u} {β : Sort v} {p : α → Prop} {q : β → Prop} (e : α ≃ β),
(∀ (b : β), p (e.symm b) ↔ q b) → ((∀ (a : α), p a) ↔ ∀ (b : β), q b) | true |
CategoryTheory.congr_app | Mathlib.CategoryTheory.NatTrans | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F G : CategoryTheory.Functor C D} {α β : CategoryTheory.NatTrans F G}, α = β → ∀ (X : C), α.app X = β.app X | true |
Fintype.linearIndependent_iffₛ | Mathlib.LinearAlgebra.LinearIndependent.Defs | ∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : Fintype ι],
LinearIndependent R v ↔ ∀ (f g : ι → R), ∑ i, f i • v i = ∑ i, g i • v i → ∀ (i : ι), f i = g i | true |
Group.nilpotencyClass_of_not_nilpotent | Mathlib.GroupTheory.Nilpotent | ∀ {G : Type u_1} [inst : Group G], ¬Group.IsNilpotent G → Group.nilpotencyClass G = 0 | true |
CategoryTheory.Functor.PreservesLeftKanExtension.mk._flat_ctor | Mathlib.CategoryTheory.Functor.KanExtension.Preserves | ∀ {A : Type u_1} {B : Type u_2} {C : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} A]
[inst_1 : CategoryTheory.Category.{v_2, u_2} B] [inst_2 : CategoryTheory.Category.{v_3, u_3} C]
[inst_3 : CategoryTheory.Category.{v_4, u_4} D] {G : CategoryTheory.Functor B D} {F : CategoryTheory.Functor A B... | false |
_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_7 | Mathlib.Data.List.Cycle | ∀ {α : Type u_1} [inst : DecidableEq α] {l : List α} {a : α},
a ∈ l →
∀ (hl : l ≠ []),
¬(List.idxOf a l + 1) % l.length + 1 ≤ l.dropLast.length →
(List.idxOf a l + 1) % l.length - l.dropLast.length < [l.getLast ⋯].length | false |
_private.Mathlib.Algebra.IsPrimePow.0.not_isPrimePow_zero._simp_1_4 | Mathlib.Algebra.IsPrimePow | ∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c) | false |
AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc | Mathlib.AlgebraicGeometry.ColimitsOver | ∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
[inst_1 : P.IsMultiplicative] {S : AlgebraicGeometry.Scheme} {J : Type u_1}
[inst_2 : CategoryTheory.Category.{v_1, u_1} J] {D : CategoryTheory.Functor J (P.Over ⊤ S)} {𝒰 : S.OpenCover}
[inst_3 : CategoryTheory.Ca... | true |
Real.expPartialHomeomorph_target | Mathlib.Analysis.SpecialFunctions.Log.Basic | Real.expPartialHomeomorph.target = Set.Ioi 0 | true |
IsCompl.compl_eq_iff | Mathlib.Order.BooleanAlgebra.Basic | ∀ {α : Type u} {x y z : α} [inst : BooleanAlgebra α], IsCompl x y → (zᶜ = y ↔ z = x) | true |
Array.all_iff_forall | Init.Data.Array.Lemmas | ∀ {α : Type u_1} {p : α → Bool} {as : Array α} {start stop : ℕ},
as.all p start stop = true ↔ ∀ (i : ℕ) (x : i < as.size), start ≤ i ∧ i < stop → p as[i] = true | true |
AddAction.sigmaFixedByEquivOrbitsProdAddGroup._proof_1 | Mathlib.GroupTheory.GroupAction.Quotient | ∀ (α : Type u_1) (β : Type u_2) [inst : AddGroup α] [inst_1 : AddAction α β] (x : α × β),
x.1 +ᵥ x.2 = x.2 ↔ x.1 +ᵥ x.2 = x.2 | false |
_private.Mathlib.Data.Rat.Sqrt.0.Rat.exists_mul_self.match_1_1 | Mathlib.Data.Rat.Sqrt | ∀ (x : ℚ) (motive : (∃ q, q * q = x) → Prop) (x_1 : ∃ q, q * q = x), (∀ (n : ℚ) (hn : n * n = x), motive ⋯) → motive x_1 | false |
Mathlib.Tactic._aux_Mathlib_Tactic_Core___macroRules_Mathlib_Tactic_tacticRepeat1__1 | Mathlib.Tactic.Core | Lean.Macro | false |
AlgebraicGeometry.instAddCommGroupObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType | Mathlib.AlgebraicGeometry.StructureSheaf | {R M : Type u} →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] →
[inst_2 : Module R M] →
(U : (TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R))ᵒᵖ) →
AddCommGroup ((AlgebraicGeometry.structureSheafInType R M).obj.obj U) | true |
HahnSeries.toOrderTopSubOnePos | Mathlib.RingTheory.HahnSeries.Summable | {Γ : Type u_1} →
{R : Type u_3} →
[inst : AddCommMonoid Γ] →
[inst_1 : LinearOrder Γ] →
[inst_2 : IsOrderedCancelAddMonoid Γ] →
[inst_3 : CommRing R] → {x : HahnSeries Γ R} → 0 < (x - 1).orderTop → ↥(HahnSeries.orderTopSubOnePos Γ R) | true |
infEDist_inv | Mathlib.Analysis.Normed.Group.Pointwise | ∀ {E : Type u_1} [inst : SeminormedCommGroup E] (x : E) (s : Set E), Metric.infEDist x⁻¹ s = Metric.infEDist x s⁻¹ | true |
instBornologyPUnit._proof_1 | Mathlib.Topology.Bornology.Basic | ⊥ ≤ Filter.cofinite | false |
Lean.SerialMessage.ctorIdx | Lean.Message | Lean.SerialMessage → ℕ | false |
Char.lt | Init.Data.Char.Basic | Char → Char → Prop | true |
Lean.Grind.CommRing.Stepwise.div_cert.eq_1 | Init.Grind.Ring.CommSolver | ∀ (p₁ : Lean.Grind.CommRing.Poly) (k : ℤ) (p : Lean.Grind.CommRing.Poly),
Lean.Grind.CommRing.Stepwise.div_cert p₁ k p = (!k.beq' 0).and' ((Lean.Grind.CommRing.Poly.mulConst_k k p).beq' p₁) | true |
_private.Lean.Shell.0.Lean.displayHelp | Lean.Shell | Bool → IO Unit | true |
_private.Mathlib.FieldTheory.AlgebraicClosure.0.le_algebraicClosure_iff._simp_1_1 | Mathlib.FieldTheory.AlgebraicClosure | ∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
(x ∈ algebraicClosure F E) = IsAlgebraic F x | false |
_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.disjoint_base_iUnion_openCell._simp_1_2 | Mathlib.Topology.CWComplex.Classical.Basic | ∀ {α : Type u_1} {ι : Sort u_5} {s : ι → Set α}, (⋃ i, s i = ∅) = ∀ (i : ι), s i = ∅ | false |
Array.forIn' | Init.Data.Array.Basic | {α : Type u} →
{β : Type v} → {m : Type v → Type w} → [Monad m] → (as : Array α) → β → ((a : α) → a ∈ as → β → m (ForInStep β)) → m β | true |
Std.ExtDTreeMap.Const.getEntryLT._proof_1 | Std.Data.ExtDTreeMap.Basic | ∀ {α : Type u_1} {cmp : α → α → Ordering} {β : Type u_2} [inst : Std.TransCmp cmp]
(t : Std.ExtDTreeMap α (fun x => β) cmp) (k : α),
(∃ a ∈ t, cmp a k = Ordering.lt) →
∀ (m : Std.DTreeMap α (fun x => β) cmp),
t = Std.ExtDTreeMap.mk m → ∃ a ∈ Std.ExtDTreeMap.mk m, cmp a k = Ordering.lt | false |
Real.logb_neg_of_base_lt_one | Mathlib.Analysis.SpecialFunctions.Log.Base | ∀ {b x : ℝ}, 0 < b → b < 1 → 1 < x → Real.logb b x < 0 | true |
CategoryTheory.equivEssImageOfReflective_inverse | Mathlib.CategoryTheory.Adjunction.Reflective | ∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{i : CategoryTheory.Functor D C} [inst_2 : CategoryTheory.Reflective i],
CategoryTheory.equivEssImageOfReflective.inverse = i.essImage.ι.comp (CategoryTheory.reflector i) | true |
AddEquiv.mk.sizeOf_spec | Mathlib.Algebra.Group.Equiv.Defs | ∀ {A : Type u_9} {B : Type u_10} [inst : Add A] [inst_1 : Add B] [inst_2 : SizeOf A] [inst_3 : SizeOf B]
(toEquiv : A ≃ B) (map_add' : ∀ (x y : A), toEquiv.toFun (x + y) = toEquiv.toFun x + toEquiv.toFun y),
sizeOf { toEquiv := toEquiv, map_add' := map_add' } = 1 + sizeOf toEquiv | true |
HomotopicalAlgebra.LeftHomotopyRel.postcomp | Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C}
[inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] {f g : X ⟶ Y},
HomotopicalAlgebra.LeftHomotopyRel f g →
∀ {Z : C} (p : Y ⟶ Z),
HomotopicalAlgebra.LeftHomotopyRel (CategoryTheory.CategoryStruct.comp f p)
(CategoryTheory... | true |
_private.Init.Data.String.Basic.0.String.Pos.toSlice_le._simp_1_1 | Init.Data.String.Basic | ∀ {s : String.Slice} {l r : s.Pos}, (l ≤ r) = (l.offset ≤ r.offset) | false |
HomologicalComplex₂.D₁_totalShift₂XIso_hom | Mathlib.Algebra.Homology.TotalComplexShift | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
(K : HomologicalComplex₂ C (ComplexShape.up ℤ) (ComplexShape.up ℤ)) (y : ℤ) [inst_2 : K.HasTotal (ComplexShape.up ℤ)]
(n₀ n₁ n₀' n₁' : ℤ) (h₀ : n₀ + y = n₀') (h₁ : n₁ + y = n₁'),
CategoryTheory.CategoryStruct.co... | true |
ByteArray.extract_eq_empty_iff | Init.Data.ByteArray.Lemmas | ∀ {b : ByteArray} {i j : ℕ}, b.extract i j = ByteArray.empty ↔ min j b.size ≤ i | true |
_private.Mathlib.RingTheory.Ideal.GoingUp.0.Ideal.IsIntegralClosure.comap_ne_bot.match_1_1 | Mathlib.RingTheory.Ideal.GoingUp | ∀ {A : Type u_1} [inst : CommRing A] {I : Ideal A} (motive : (∃ x ∈ I, x ≠ 0) → Prop) (x : ∃ x ∈ I, x ≠ 0),
(∀ (x : A) (x_mem : x ∈ I) (x_ne_zero : x ≠ 0), motive ⋯) → motive x | false |
Lean.instInhabitedAuxParentProjectionInfo.default | Lean.ProjFns | Lean.AuxParentProjectionInfo | true |
_private.Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension.0.IsOpen.exists_contDiff_support_eq._simp_1_1 | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | ∀ {α : Type u_1} {a : α} {s : Set α}, ({a} ⊆ s) = (a ∈ s) | false |
Mathlib.Tactic.Coherence._aux_Mathlib_Tactic_CategoryTheory_Coherence___elabRules_Mathlib_Tactic_Coherence_pure_coherence_internal_1 | Mathlib.Tactic.CategoryTheory.Coherence | Lean.Elab.Tactic.Tactic | false |
_private.Aesop.Forward.State.0.Aesop.instBEqRawHyp.beq.match_1 | Aesop.Forward.State | (motive : Aesop.RawHyp → Aesop.RawHyp → Sort u_1) →
(x x_1 : Aesop.RawHyp) →
((a b : Lean.FVarId) → motive (Aesop.RawHyp.fvarId a) (Aesop.RawHyp.fvarId b)) →
((a b : Aesop.Substitution) → motive (Aesop.RawHyp.patSubst a) (Aesop.RawHyp.patSubst b)) →
((x x_2 : Aesop.RawHyp) → motive x x_2) → motive x... | false |
CategoryTheory.Monad.id._proof_1 | Mathlib.CategoryTheory.Monad.Basic | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] (X : C),
CategoryTheory.CategoryStruct.comp
((CategoryTheory.Functor.id C).map ((CategoryTheory.CategoryStruct.id (CategoryTheory.Functor.id C)).app X))
((CategoryTheory.CategoryStruct.id (CategoryTheory.Functor.id C)).app X) =
CategoryThe... | false |
ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map₀ | Mathlib.Probability.Independence.Basic | ∀ {Ω : Type u_7} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {M : Type u_10} [inst : Monoid M]
[inst_1 : MeasurableSpace M] [MeasurableMul₂ M] [MeasureTheory.IsFiniteMeasure μ] {f g : Ω → M},
AEMeasurable f μ →
AEMeasurable g μ →
ProbabilityTheory.IndepFun f g μ →
MeasureTheory.Measure.... | true |
multiplicity_addValuation_apply | Mathlib.RingTheory.Valuation.PrimeMultiplicity | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {p : R} {hp : Prime p} {r : R},
(multiplicity_addValuation hp) r = emultiplicity p r | true |
ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt | Mathlib.Analysis.ODE.PicardLindelof | ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {f : E → E} {x₀ : E},
ContDiffAt ℝ 1 f x₀ →
∀ (t₀ : ℝ),
∃ r > 0,
∃ ε > 0, ∀ x ∈ Metric.closedBall x₀ r, ∃ α, α t₀ = x ∧ ∀ t ∈ Set.Ioo (t₀ - ε) (t₀ + ε), HasDerivAt α (f (α t)) t | true |
Path.Homotopy.transAssoc._proof_4 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | ⟨Path.Homotopy.transAssocReparamAux 1, Path.Homotopy.transAssoc._proof_3⟩ = 1 | false |
Std.Tactic.BVDecide.Normalize.BitVec.beq_one_eq_ite' | Std.Tactic.BVDecide.Normalize.Bool | ∀ {b : Bool} {a : BitVec 1}, (b == (a == 1#1)) = (a == bif b then 1#1 else 0#1) | true |
HasFibers.instFaithfulFibι | Mathlib.CategoryTheory.FiberedCategory.HasFibers | ∀ {𝒮 : Type u₁} {𝒳 : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} 𝒮] [inst_1 : CategoryTheory.Category.{v₂, u₂} 𝒳]
(p : CategoryTheory.Functor 𝒳 𝒮) [inst_2 : HasFibers p] (S : 𝒮), (HasFibers.ι S).Faithful | true |
CategoryTheory.InjectiveResolution.toRightDerivedZero'._proof_2 | Mathlib.CategoryTheory.Abelian.RightDerived | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
[inst_1 : CategoryTheory.Category.{u_1, u_2} D] [inst_2 : CategoryTheory.Abelian C]
[inst_3 : CategoryTheory.Abelian D] {X : C} (P : CategoryTheory.InjectiveResolution X)
(F : CategoryTheory.Functor C D) [inst_4 : F.Additive],
Categor... | false |
instCategoryCompactum._proof_9 | Mathlib.Topology.Category.Compactum | autoParam
(∀ {W X Y Z : Compactum} (f : W ⟶ X) (g : X ⟶ Y) (h : Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h =
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp g h))
CategoryTheory.Category.assoc._autoParam | false |
CategoryTheory.ParametrizedAdjunction.rec | Mathlib.CategoryTheory.Adjunction.Parametrized | {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 ... | false |
Turing.PartrecToTM2.tr.eq_2 | Mathlib.Computability.TuringMachine.ToPartrec | ∀ (k : Turing.PartrecToTM2.K') (f : Option Turing.PartrecToTM2.Γ' → Option Turing.PartrecToTM2.Γ')
(q : Turing.PartrecToTM2.Λ'),
Turing.PartrecToTM2.tr (Turing.PartrecToTM2.Λ'.push k f q) =
Turing.TM2.Stmt.branch (fun s => (f s).isSome)
(Turing.TM2.Stmt.push k (fun s => (f s).getD default) (Turing.TM2.Stm... | true |
Std.DTreeMap.getKeyD_minKey! | Std.Data.DTreeMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t : Std.DTreeMap α β cmp} [Std.TransCmp cmp]
[inst : Inhabited α], t.isEmpty = false → ∀ {fallback : α}, t.getKeyD t.minKey! fallback = t.minKey! | true |
PMF.seq.eq_1 | Mathlib.Probability.ProbabilityMassFunction.Constructions | ∀ {α : Type u_1} {β : Type u_2} (q : PMF (α → β)) (p : PMF α), q.seq p = q.bind fun m => p.bind fun a => PMF.pure (m a) | true |
Lean.Elab.Tactic.BVDecide.Frontend.SolverMode._sizeOf_1 | Std.Tactic.BVDecide.Syntax | Lean.Elab.Tactic.BVDecide.Frontend.SolverMode → ℕ | false |
Equiv.addEquiv._proof_1 | Mathlib.Algebra.Group.TransferInstance | ∀ {α : Type u_2} {β : Type u_1} (e : α ≃ β) [inst : Add β] (x y : α), e.toFun (x + y) = e.toFun x + e.toFun y | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | ∀ {α : Type u_1} {l₁ l₂ : List α}, l₁ <+: l₂ → (l₁ <:+: l₂) = True | false |
CategoryTheory.yonedaAddMon._proof_5 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_ | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
(M : CategoryTheory.AddMon C) (Y : Cᵒᵖ) (φ₁ φ₂ : Opposite.unop Y ⟶ M.X),
CategoryTheory.CategoryStruct.comp (φ₁ + φ₂) (CategoryTheory.CategoryStruct.id M).hom =
CategoryTheory.CategoryStruct.comp... | false |
SupIrred.ne_bot | Mathlib.Order.Irreducible | ∀ {α : Type u_2} [inst : SemilatticeSup α] {a : α} [inst_1 : OrderBot α], SupIrred a → a ≠ ⊥ | true |
HomologicalComplex.mapBifunctor₂₃.d₃_eq | Mathlib.Algebra.Homology.BifunctorAssociator | ∀ {C₁ : Type u_1} {C₂ : Type u_2} {C₂₃ : Type u_4} {C₃ : Type u_5} {C₄ : Type u_6}
[inst : CategoryTheory.Category.{v_1, u_1} C₁] [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂]
[inst_2 : CategoryTheory.Category.{v_3, u_5} C₃] [inst_3 : CategoryTheory.Category.{v_4, u_6} C₄]
[inst_4 : CategoryTheory.Category.{v_... | true |
Set.nonempty_sInter._simp_1 | Mathlib.Data.Set.Lattice | ∀ {α : Type u_1} {c : Set (Set α)}, (⋂₀ c).Nonempty = ∃ a, ∀ b ∈ c, a ∈ b | false |
_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ofPrime_idealOfLE._simp_1_2 | Mathlib.RingTheory.Valuation.ValuationSubring | ∀ {M : Type u_1} [inst : MulOneClass M] {s : Subsemigroup M} {x : M} (h_one : 1 ∈ s.carrier),
(x ∈ { toSubsemigroup := s, one_mem' := h_one }) = (x ∈ s) | false |
DirSupInaccOn | Mathlib.Order.DirSupClosed | {α : Type u_1} → [Preorder α] → Set (Set α) → Set α → Prop | true |
extDeriv_apply_vectorField_of_pairwise_commute | Mathlib.Analysis.Calculus.DifferentialForm.VectorField | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ} {x : E}
{ω : E → E [⋀^Fin n]→L[𝕜] F} {V : Fin (n + 1) → E → E},
DifferentiableAt 𝕜 ω x →
(∀ (i :... | true |
BitVec.toNat_cpop_concat | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {x : BitVec w} {b : Bool}, (x.concat b).cpop.toNat = b.toNat + x.cpop.toNat | true |
Polynomial.recOnHorner._unary._proof_15 | Mathlib.Algebra.Polynomial.Inductions | ∀ {R : Type u_2} [inst : Semiring R] {M : Polynomial R → Sort u_1} (p : Polynomial R),
M (p.divX * Polynomial.X + Polynomial.C 0) = M (p.divX * Polynomial.X + 0) | false |
Aesop.instInhabitedNormalizationState.default | Aesop.Tree.Data | Aesop.NormalizationState | true |
_private.Std.Data.DHashMap.Lemmas.0.Std.DHashMap.mem_alter._simp_1_1 | Std.Data.DHashMap.Lemmas | ∀ {α : Type u} {β : α → Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.DHashMap α β} {a : α},
(a ∈ m) = (m.contains a = true) | false |
DifferentiableOn.mul_const | Mathlib.Analysis.Calculus.FDeriv.Mul | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {s : Set E} {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸]
{a : E → 𝔸}, DifferentiableOn 𝕜 a s → ∀ (b : 𝔸), DifferentiableOn 𝕜 (fun y => a y * b) s | true |
CategoryTheory.Limits.KernelFork.IsLimit.ofιUnop._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{K X Y : Cᵒᵖ} (i : K ⟶ X) {f : X ⟶ Y} (w : CategoryTheory.CategoryStruct.comp i f = 0)
(h : CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.KernelFork.ofι i w)) {Z' : C} (x : Opposite.unop X ⟶ Z')... | false |
FiniteField.frobeniusAlgEquiv._proof_1 | Mathlib.FieldTheory.Finite.Basic | ∀ (K : Type u_2) (R : Type u_1) [inst : Field K] [inst_1 : Fintype K] [inst_2 : CommRing R] [inst_3 : Algebra K R]
(p : ℕ) [ExpChar R p] [PerfectRing R p], Function.Bijective ⇑(FiniteField.frobeniusAlgHom K R) | false |
UniformSpace.Completion.extensionHom._proof_2 | Mathlib.Topology.Algebra.UniformRing | ∀ {α : Type u_2} [inst : Ring α] {β : Type u_1} [inst_1 : Ring β], AddMonoidHomClass (α →+* β) α β | false |
_private.Batteries.Data.List.Lemmas.0.List.pos_findIdxNth_getElem._proof_1_12 | Batteries.Data.List.Lemmas | ∀ {α : Type u_1} {p : α → Bool} (tail : List α) {n : ℕ},
List.findIdxNth p tail (n - 1) + 1 ≤ tail.length → List.findIdxNth p tail (n - 1) < tail.length | false |
_private.Lean.Data.FuzzyMatching.0.Lean.FuzzyMatching.Score | Lean.Data.FuzzyMatching | Type | true |
_private.Qq.Macro.0.Qq.Impl.quoteExpr.match_1 | Qq.Macro | (motive : Qq.Impl.ExprBackSubstResult → Sort u_1) →
(r : Qq.Impl.ExprBackSubstResult) →
((r : Lean.Expr) → motive (Qq.Impl.ExprBackSubstResult.quoted r)) →
((r : Lean.Expr) → motive (Qq.Impl.ExprBackSubstResult.unquoted r)) → motive r | false |
FreeLieAlgebra.lift_of_apply | Mathlib.Algebra.Lie.Free | ∀ {R : Type u} {X : Type v} [inst : CommRing R] {L : Type w} [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (f : X → L)
(x : X), ((FreeLieAlgebra.lift R) f) (FreeLieAlgebra.of R x) = f x | true |
CategoryTheory.SplitMono | Mathlib.CategoryTheory.EpiMono | {C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ⟶ Y) → Type v₁ | true |
instAlgebraUniversalEnvelopingAlgebra._aux_1 | Mathlib.Algebra.Lie.UniversalEnveloping | (R : Type u_1) →
(L : Type u_2) →
[inst : CommRing R] →
[inst_1 : LieRing L] →
[inst_2 : LieAlgebra R L] → R → UniversalEnvelopingAlgebra R L → UniversalEnvelopingAlgebra R L | false |
MDifferentiableWithinAt.prodMap' | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | ∀ {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... | true |
CategoryTheory.Localization.Construction.morphismProperty_eq_top' | Mathlib.CategoryTheory.Localization.Construction | ∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] {W : CategoryTheory.MorphismProperty C}
(P : CategoryTheory.MorphismProperty W.Localization) [P.IsStableUnderComposition],
(∀ ⦃X Y : C⦄ (f : X ⟶ Y), P (W.Q.map f)) → (∀ ⦃X Y : W.Localization⦄ (e : X ≅ Y), P e.hom → P e.inv) → P = ⊤ | true |
FreeGroup.of_ne_one._simp_2 | Mathlib.GroupTheory.FreeGroup.Reduce | ∀ {α : Type u_1} (a : α), (FreeGroup.of a = 1) = False | false |
Lean.TSyntax.ctorIdx | Init.Prelude | {ks : Lean.SyntaxNodeKinds} → Lean.TSyntax ks → ℕ | false |
_private.Mathlib.Algebra.Algebra.Subalgebra.Basic.0.Subalgebra.isDomain._proof_1 | Mathlib.Algebra.Algebra.Subalgebra.Basic | ∀ {R : Type u_2} {A : Type u_1} [inst : CommRing R] [inst_1 : Ring A] [IsDomain A] [inst_3 : Algebra R A]
(S : Subalgebra R A), IsDomain ↥S | false |
AddEquiv.toMultiplicativeLeft._proof_7 | Mathlib.Algebra.Group.Equiv.TypeTags | ∀ {G : Type u_1} {H : Type u_2} [inst : AddZeroClass G] [inst_1 : MulOneClass H] (f : Multiplicative G ≃* H),
Function.RightInverse f.invFun f.toFun | false |
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