name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Firefox.Milliseconds.mk.sizeOf_spec | Lean.Util.Profiler | ∀ (ms : Float), sizeOf { ms := ms } = 1 + sizeOf ms | true |
Float.toInt32 | Init.Data.SInt.Float | Float → Int32 | true |
HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId._proof_3 | Mathlib.Algebra.Homology.Double | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] {ι : Type u_1} {c : ComplexShape ι} {i₀ i₁ : ι} (hi₀₁ : c.Rel i₀ i₁)
(h : i₀ ≠ i₁) (X : C) {K : HomologicalComplex C c}
(g : HomologicalComplex.double... | false |
IsUnit.mul_div_mul_left | Mathlib.Algebra.Group.Units.Defs | ∀ {α : Type u} [inst : DivisionCommMonoid α] {c : α}, IsUnit c → ∀ (a b : α), c * a / (c * b) = a / b | true |
Std.DTreeMap.Internal.Impl.getEntryLT?.go.match_1 | Std.Data.DTreeMap.Internal.Queries | (motive : Ordering → Sort u_1) → (x : Ordering) → (Unit → motive Ordering.gt) → ((x : Ordering) → motive x) → motive x | false |
Lean.Widget.InteractiveTermGoal.term | Lean.Widget.InteractiveGoal | Lean.Widget.InteractiveTermGoal → Lean.Server.WithRpcRef Lean.Elab.TermInfo | true |
Monovary.of_inv_left | Mathlib.Algebra.Order.Monovary | ∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : CommGroup α] [inst_1 : Preorder α] [IsOrderedMonoid α]
[inst_3 : PartialOrder β] {f : ι → α} {g : ι → β}, Monovary f⁻¹ g → Antivary f g | true |
Metric.IsSeparated.of_subsingleton | Mathlib.Topology.MetricSpace.MetricSeparated | ∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {s : Set X} {ε : ENNReal}, s.Subsingleton → Metric.IsSeparated ε s | true |
Prod.exists | Init.Data.Prod | ∀ {α : Type u_1} {β : Type u_2} {p : α × β → Prop}, (∃ x, p x) ↔ ∃ a b, p (a, b) | true |
Std.HashMap.length_keys | Std.Data.HashMap.Lemmas | ∀ {α : Type u} {β : Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.HashMap α β} [EquivBEq α] [LawfulHashable α],
m.keys.length = m.size | true |
instDecidableEqQuaternionGroup.decEq._proof_1 | Mathlib.GroupTheory.SpecificGroups.Quaternion | ∀ {n : ℕ} (a : ZMod (2 * n)), QuaternionGroup.a a = QuaternionGroup.a a | false |
CondensedSet.isDiscrete_tfae | Mathlib.Condensed.Discrete.Characterization | ∀ (X : CondensedSet),
[Condensed.IsDiscrete X, CategoryTheory.IsIso ((Condensed.discreteUnderlyingAdj (Type (u + 1))).counit.app X),
(Condensed.discrete (Type (u + 1))).essImage X, CondensedSet.LocallyConstant.functor.essImage X,
CategoryTheory.IsIso (CondensedSet.LocallyConstant.adjunction.counit.app X),... | true |
CategoryTheory.Functor.leftOpRightOpEquiv._proof_6 | Mathlib.CategoryTheory.Opposites | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_4, u_2} C] (D : Type u_1)
[inst_1 : CategoryTheory.Category.{u_3, u_1} D] {X Y : (CategoryTheory.Functor Cᵒᵖ D)ᵒᵖ} (f : X ⟶ Y),
CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id (CategoryTheory.Functor Cᵒᵖ D)ᵒᵖ).map f)
((fun F => (Opposite.unop ... | false |
_private.Mathlib.Analysis.SpecialFunctions.Pow.Deriv.0.Real.deriv_rpow_const._proof_1_1 | Mathlib.Analysis.SpecialFunctions.Pow.Deriv | ∀ (x p : ℝ), p ≠ 0 → x = 0 ∧ p < 1 → deriv (fun x => x ^ p) 0 = 0 → deriv (fun x => x ^ p) x = p * x ^ (p - 1) | false |
_private.Mathlib.Data.Nat.Choose.Basic.0.Nat.choose_ne_zero_iff._simp_1_1 | Mathlib.Data.Nat.Choose.Basic | ∀ {n k : ℕ}, (n.choose k = 0) = (n < k) | false |
Lean.IR.instToStringExpr | Lean.Compiler.IR.Format | ToString Lean.IR.Expr | true |
AlgebraicGeometry.functionField_isFractionRing_of_affine | Mathlib.AlgebraicGeometry.FunctionField | ∀ (R : CommRingCat) [inst : IsDomain ↑R], IsFractionRing ↑R ↑(AlgebraicGeometry.Spec R).functionField | true |
UniqueFactorizationMonoid.radical.eq_1 | Mathlib.RingTheory.Radical.Basic | ∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
(a : M), UniqueFactorizationMonoid.radical a = (UniqueFactorizationMonoid.primeFactors a).prod id | true |
GromovHausdorff.premetricOptimalGHDist._proof_3 | Mathlib.Topology.MetricSpace.GromovHausdorffRealized | ∀ (X : Type u_1) (Y : Type u_2) [inst : MetricSpace X] [inst_1 : CompactSpace X] [inst_2 : Nonempty X]
[inst_3 : MetricSpace Y] [inst_4 : CompactSpace Y] [inst_5 : Nonempty Y],
(Bornology.cobounded (X ⊕ Y)).sets = {s | ∃ C, ∀ x ∈ sᶜ, ∀ y ∈ sᶜ, (GromovHausdorff.optimalGHDist✝ X Y) (x, y) ≤ C} | false |
Fin.OrderEmbedding.default_def | Mathlib.Order.Fin.Basic | ∀ {n : ℕ}, default = Fin.valOrderEmb n | true |
Path.Homotopy.reflTrans._proof_1 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | ∀ {X : Type u_1} [inst : TopologicalSpace X] {x₀ x₁ : X} (p : Path x₀ x₁),
(p.symm.trans (Path.refl x₀)).symm = (Path.refl x₀).trans p | false |
HomotopicalAlgebra.BifibrantObject.weakEquivalence_homMk_iff | Mathlib.AlgebraicTopology.ModelCategory.Bifibrant | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
[inst_2 : CategoryTheory.Limits.HasInitial C] [inst_3 : HomotopicalAlgebra.CategoryWithFibrations C]
[inst_4 : CategoryTheory.Limits.HasTerminal C] [inst_5 : HomotopicalAlgebra.CategoryWithWeakEquivalen... | true |
CategoryTheory.Pairwise.Hom.right.elim | Mathlib.CategoryTheory.Category.Pairwise | {ι : Type v} →
{motive : (a a_1 : CategoryTheory.Pairwise ι) → a.Hom a_1 → Sort u} →
{a a_1 : CategoryTheory.Pairwise ι} →
(t : a.Hom a_1) →
t.ctorIdx = 3 →
((i j : ι) →
motive (CategoryTheory.Pairwise.pair i j) (CategoryTheory.Pairwise.single j)
(CategoryTheo... | false |
_private.Init.Data.Range.Polymorphic.SInt.0.Int64.instUpwardEnumerable_eq | Init.Data.Range.Polymorphic.SInt | Int64.instUpwardEnumerable = HasModel.instUpwardEnumerable✝ | true |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Besicovitch.TauPackage.color_lt._simp_1_8 | Mathlib.MeasureTheory.Covering.Besicovitch | ∀ {α : Type u} {s t : Set α} (x : α), (x ∈ s \ t) = (x ∈ s ∧ x ∉ t) | false |
Lean.IR.instToFormatParam._private_1 | Lean.Compiler.IR.Format | Lean.IR.Param → Std.Format | false |
_private.Init.Data.List.MapIdx.0.List.mapFinIdx_eq_append_iff._proof_1_7 | Init.Data.List.MapIdx | ∀ {α : Type u_2} {β : Type u_1} {l₁ l₂ : List β} {l : List α} {f : (i : ℕ) → α → i < l.length → β},
l₁.length + l₂.length = l.length → ∀ i < l₂.length, ¬i + l₁.length < l.length → False | false |
Finsupp.sumFinsuppEquivProdFinsupp_symm_apply | Mathlib.Data.Finsupp.Basic | ∀ {α : Type u_12} {β : Type u_13} {γ : Type u_14} [inst : Zero γ] (fg : (α →₀ γ) × (β →₀ γ)),
Finsupp.sumFinsuppEquivProdFinsupp.symm fg = fg.1.sumElim fg.2 | true |
_private.Mathlib.Analysis.BoxIntegral.UnitPartition.0.BoxIntegral.unitPartition.termL | Mathlib.Analysis.BoxIntegral.UnitPartition | Lean.ParserDescr | true |
SheafOfModules.restrictScalars | Mathlib.Algebra.Category.ModuleCat.Sheaf.ChangeOfRings | {C : Type u'} →
[inst : CategoryTheory.Category.{v', u'} C] →
{J : CategoryTheory.GrothendieckTopology C} →
{R R' : CategoryTheory.Sheaf J RingCat} → (R ⟶ R') → CategoryTheory.Functor (SheafOfModules R') (SheafOfModules R) | true |
Quiver.SingleObj.toPrefunctor | Mathlib.Combinatorics.Quiver.SingleObj | {α : Type u_1} → {β : Type u_2} → (α → β) ≃ Quiver.SingleObj α ⥤q Quiver.SingleObj β | true |
_private.Mathlib.Analysis.Distribution.SchwartzSpace.Basic.0.SchwartzMap.denseRange_toLpCLM._simp_1_4 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | ∀ {α : Sort u_2} {β : Sort u_1} (f : α → β) (a' : α), (∃ a, f a = f a') = True | false |
_private.Mathlib.Analysis.Calculus.Rademacher.0.LipschitzWith.ae_lineDeriv_sum_eq._simp_1_2 | Mathlib.Analysis.Calculus.Rademacher | ∀ {G : Type u_3} [inst : InvolutiveNeg G] {a b : G}, (-a = -b) = (a = b) | false |
CategoryTheory.Triangulated.TStructure.isLE_shift_iff | Mathlib.CategoryTheory.Triangulated.TStructure.Basic | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ]
[inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
(t : CategoryT... | true |
Mathlib.Tactic.BicategoryLike.MonadWhiskerRight.casesOn | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | {m : Type → Type} →
{motive : Mathlib.Tactic.BicategoryLike.MonadWhiskerRight m → Sort u} →
(t : Mathlib.Tactic.BicategoryLike.MonadWhiskerRight m) →
((whiskerRightM :
Mathlib.Tactic.BicategoryLike.WhiskerRight →
Mathlib.Tactic.BicategoryLike.Atom₁ → m Mathlib.Tactic.BicategoryLike... | false |
HahnSeries.SummableFamily.smul._proof_1 | Mathlib.RingTheory.HahnSeries.Summable | ∀ {Γ : Type u_6} {Γ' : Type u_1} {R : Type u_5} {V : Type u_4} {α : Type u_2} {β : Type u_3} [inst : PartialOrder Γ]
[inst_1 : PartialOrder Γ'] [inst_2 : AddCommMonoid V] [inst_3 : AddCommMonoid R] [inst_4 : SMulWithZero R V]
[inst_5 : VAdd Γ Γ'] [inst_6 : IsOrderedCancelVAdd Γ Γ'] (s : HahnSeries.SummableFamily Γ ... | false |
nontrivial_of_ne | Mathlib.Logic.Nontrivial.Defs | ∀ {α : Type u_1} (x y : α), x ≠ y → Nontrivial α | true |
Mathlib.Tactic.Ring.Common.ExSum.below | Mathlib.Tactic.Ring.Common | {u : Lean.Level} →
{α : Q(Type u)} →
{BaseType : Q(«$α») → Type} →
{sα : Q(CommSemiring «$α»)} →
{motive_1 : (e : Q(«$α»)) → Mathlib.Tactic.Ring.Common.ExBase BaseType sα e → Sort u} →
{motive_2 : (e : Q(«$α»)) → Mathlib.Tactic.Ring.Common.ExProd BaseType sα e → Sort u} →
{moti... | false |
Algebra.QuasiFinite.trans | Mathlib.RingTheory.QuasiFinite.Basic | ∀ (R : Type u_1) (S : Type u_2) (T : Type u_3) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] [Algebra.QuasiFinite R S]
[Algebra.QuasiFinite S T], Algebra.QuasiFinite R T | true |
CategoryTheory.Abelian.SpectralObject.mono_H_map_twoδ₁Toδ₀ | Mathlib.Algebra.Homology.SpectralObject.Basic | ∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{u_3, u_1} C]
[inst_1 : CategoryTheory.Category.{u_4, u_2} ι] [inst_2 : CategoryTheory.Abelian C]
(X : CategoryTheory.Abelian.SpectralObject C ι) (n₀ : ℤ) {i₀ i₁ i₂ : ι} (f : i₀ ⟶ i₁) (g : i₁ ⟶ i₂) (fg : i₀ ⟶ i₂)
(hfg : CategoryTheory.CategoryStruct.... | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.Ext.ExtClass.0.CategoryTheory.ShortComplex.ShortExact._aux_Mathlib_Algebra_Homology_DerivedCategory_Ext_ExtClass___unexpand_CochainComplex_mappingCone_quasiIso_descShortComplex_1 | Mathlib.Algebra.Homology.DerivedCategory.Ext.ExtClass | Lean.PrettyPrinter.Unexpander | false |
Batteries.Tactic.Lint.Linter._sizeOf_1 | Batteries.Tactic.Lint.Basic | Batteries.Tactic.Lint.Linter → ℕ | false |
CategoryTheory.IsPushout.inl_isoIsPushout_inv_assoc | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Z : C} (X Y : C) {P : C} {f : Z ⟶ X} {g : Z ⟶ Y}
{inl : X ⟶ P} {inr : Y ⟶ P} {P' : C} {inl' : X ⟶ P'} {inr' : Y ⟶ P'} (h : CategoryTheory.IsPushout f g inl inr)
(h' : CategoryTheory.IsPushout f g inl' inr') {Z_1 : C} (h_1 : P ⟶ Z_1),
CategoryTheory.Cate... | true |
Submodule.range_liftQ | Mathlib.LinearAlgebra.Quotient.Basic | ∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M)
{R₂ : Type u_3} {M₂ : Type u_4} [inst_3 : Ring R₂] [inst_4 : AddCommGroup M₂] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
[inst_6 : RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ f.ker), (p.liftQ f ... | true |
List.isChain_pmap_of_isChain | Mathlib.Data.List.Chain | ∀ {α : Type u} {β : Type v} {R : α → α → Prop} {S : β → β → Prop} {p : α → Prop} {f : (a : α) → p a → β},
(∀ (a b : α) (ha : p a) (hb : p b), R a b → S (f a ha) (f b hb)) →
∀ {l : List α}, List.IsChain R l → ∀ (hl₂ : ∀ a ∈ l, p a), List.IsChain S (List.pmap f l hl₂) | true |
TensorProduct.LieModule.lieRingModule._proof_1 | Mathlib.Algebra.Lie.TensorProduct | ∀ {R : Type u_1} [inst : CommRing R] {L : Type u_4} {M : Type u_2} {N : Type u_3} [inst_1 : LieRing L]
[inst_2 : LieAlgebra R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M]
[inst_6 : LieModule R L M] [inst_7 : AddCommGroup N] [inst_8 : Module R N] [inst_9 : LieRingModule L N]
[ins... | false |
Lean.Elab.Modifiers | Lean.Elab.DeclModifiers | Type | true |
Lean.DeclNameGenerator.parentIdxs._default | Lean.CoreM | List ℕ | false |
Submodule.mem_sup' | Mathlib.LinearAlgebra.Span.Defs | ∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : M}
{p p' : Submodule R M}, x ∈ p ⊔ p' ↔ ∃ y z, ↑y + ↑z = x | true |
Aesop.instEmptyCollectionState | Aesop.BaseM | EmptyCollection Aesop.BaseM.State | true |
_private.Init.Data.List.Nat.Basic.0.List.filterMap.match_1.eq_1 | Init.Data.List.Nat.Basic | ∀ {β : Type u_1} (motive : Option β → Sort u_2) (h_1 : Unit → motive none) (h_2 : (b : β) → motive (some b)),
(match none with
| none => h_1 ()
| some b => h_2 b) =
h_1 () | true |
Set.boolIndicator | Mathlib.Data.Set.BoolIndicator | {α : Type u_1} → Set α → α → Bool | true |
Lean.Server.RpcObjectStore._sizeOf_1 | Lean.Server.Rpc.Basic | Lean.Server.RpcObjectStore → ℕ | false |
CategoryTheory.MonoidalClosed.uncurry_pre | Mathlib.CategoryTheory.Monoidal.Closed.Basic | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {A B : C}
[inst_2 : CategoryTheory.Closed A] [inst_3 : CategoryTheory.Closed B] (f : B ⟶ A) (X : C),
CategoryTheory.MonoidalClosed.uncurry ((CategoryTheory.MonoidalClosed.pre f).app X) =
CategoryTheory.Category... | true |
PrimeSpectrum.instKrullDimLEOfNatNat | Mathlib.RingTheory.Spectrum.Prime.Noetherian | ∀ (R : Type u) [inst : CommRing R] [IsArtinianRing R], Ring.KrullDimLE 0 R | true |
List.sum_const_nat | Mathlib.Algebra.BigOperators.Group.List.Basic | ∀ (m n : ℕ), (List.replicate m n).sum = m * n | true |
SameRay.neg | Mathlib.LinearAlgebra.Ray | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
[inst_3 : AddCommGroup M] [inst_4 : Module R M] {x y : M}, SameRay R x y → SameRay R (-x) (-y) | true |
UInt16.left_eq_add | Init.Data.UInt.Lemmas | ∀ {a b : UInt16}, a = a + b ↔ b = 0 | true |
_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapPreimage._f | Mathlib.RingTheory.AdicCompletion.Exactness | {R : Type u} →
[inst : CommRing R] →
{I : Ideal R} →
{M : Type v} →
[inst_1 : AddCommGroup M] →
[inst_2 : Module R M] →
{N : Type w} →
[inst_3 : AddCommGroup N] →
[inst_4 : Module R N] →
{f : M →ₗ[R] N} →
Funct... | false |
Set.EqOn.inter_preimage_eq | Mathlib.Data.Set.Function | ∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f₁ f₂ : α → β},
Set.EqOn f₁ f₂ s → ∀ (t : Set β), s ∩ f₁ ⁻¹' t = s ∩ f₂ ⁻¹' t | true |
FractionalIdeal.spanSingleton | Mathlib.RingTheory.FractionalIdeal.Operations | {R : Type u_5} →
[inst : CommRing R] →
(S : Submonoid R) →
{P : Type u_6} → [inst_1 : CommRing P] → [inst_2 : Algebra R P] → [IsLocalization S P] → P → FractionalIdeal S P | true |
CategoryTheory.MorphismProperty.Comma.noConfusionType | Mathlib.CategoryTheory.MorphismProperty.Comma | Sort u →
{A : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} A] →
{B : Type u_2} →
[inst_1 : CategoryTheory.Category.{v_2, u_2} B] →
{T : Type u_3} →
[inst_2 : CategoryTheory.Category.{v_3, u_3} T] →
{L : CategoryTheory.Functor A T} →
{R : ... | false |
_private.Mathlib.Algebra.Module.Submodule.Lattice.0.Submodule.disjoint_iff_add_eq_zero._simp_1_1 | Mathlib.Algebra.Module.Submodule.Lattice | ∀ {R : Type u} {M : Type v} [inst : Ring R] [inst_1 : AddCommGroup M] {module_M : Module R M} (p : Submodule R M)
{x : M}, (x ∈ p) = (x ∈ p.toAddSubgroup) | false |
MultilinearMap.fromDFinsuppEquiv_single | Mathlib.LinearAlgebra.Multilinear.DFinsupp | ∀ {ι : Type uι} {κ : ι → Type uκ} {R : Type uR} {M : (i : ι) → κ i → Type uM} [inst : DecidableEq ι]
[inst_1 : Fintype ι] [inst_2 : CommSemiring R] [inst_3 : (i : ι) → (k : κ i) → AddCommMonoid (M i k)]
[inst_4 : (i : ι) → (k : κ i) → Module R (M i k)] {N : Type u_1} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]... | true |
Lean.Meta.Grind.Action.loopRef | Lean.Meta.Tactic.Grind.Action | ℕ → Lean.Meta.Grind.Action → Lean.Meta.Grind.Action | true |
QuaternionAlgebra.coe_mul._simp_1 | Mathlib.Algebra.Quaternion | ∀ {R : Type u_3} {c₁ c₂ c₃ : R} (x y : R) [inst : CommRing R], ↑x * ↑y = ↑(x * y) | false |
RootPairing.IsIrreducible.mk | Mathlib.LinearAlgebra.RootSystem.Irreducible | ∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
[inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {P : RootPairing ι R M N},
Nontrivial M →
Nontrivial N →
(∀ (q : Submodule R M), (∀ (i : ι), q ∈ Module.End.invtSubmodule ↑(P.re... | true |
MeasureTheory.dense_of_generateFrom_isSetRing | Mathlib.MeasureTheory.Measure.MeasuredSets | ∀ {α : Type u_1} [mα : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst : MeasureTheory.IsFiniteMeasure μ]
{C : Set (Set α)},
MeasureTheory.IsSetRing C →
(∃ D, D.Countable ∧ D ⊆ C ∧ μ (⋃₀ D)ᶜ = 0) → mα = MeasurableSpace.generateFrom C → Dense (SetLike.coe ⁻¹' C) | true |
CategoryTheory.Functor.preservesFiniteLimits_of_preservesKernels | Mathlib.CategoryTheory.Preadditive.LeftExact | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Preadditive C] {D : Type u₂}
[inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D)
[F.PreservesZeroMorphisms] [CategoryTheory.Limits.HasBinaryBiproducts C] [CategoryT... | true |
CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φ | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (X : CategoryTheory.Limits.FormalCoproduct C)
(x : (∐ X.toFun).I),
X.coproductIsoSelf.hom.φ x =
CategoryTheory.CategoryStruct.comp ((CategoryTheory.Limits.FormalCoproduct.coproductIsoCofanPt X.I X.toFun).hom.φ x)
(X.cofanPtIsoSelf.hom.φ ((CategoryTh... | true |
_private.Mathlib.Topology.Covering.Basic.0.IsEvenlyCovered.continuousAt.match_1_1 | Mathlib.Topology.Covering.Basic | ∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} {I : Type u_3}
[inst_2 : TopologicalSpace I] {x : E} (motive : IsEvenlyCovered f (f x) I → Prop) (h : IsEvenlyCovered f (f x) I),
(∀ (left : DiscreteTopology I) (w : Set X) (hxU : f x ∈ w) (left_1 : IsOpen w) (left... | false |
CategoryTheory.ComposableArrows.δlastFunctor | Mathlib.CategoryTheory.ComposableArrows.Basic | {C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
{n : ℕ} → CategoryTheory.Functor (CategoryTheory.ComposableArrows C (n + 1)) (CategoryTheory.ComposableArrows C n) | true |
Fin.isNone_of_isNone_findSome? | Batteries.Data.Fin.Lemmas | ∀ {n : ℕ} {α : Type u_1} {i : Fin n} {f : Fin n → Option α}, (Fin.findSome? f).isNone = true → (f i).isNone = true | true |
Algebra.FormallySmooth.pi_iff | Mathlib.RingTheory.Smooth.Pi | ∀ {R : Type u_1} {I : Type u_2} (A : I → Type u_3) [inst : CommRing R] [inst_1 : (i : I) → CommRing (A i)]
[inst_2 : (i : I) → Algebra R (A i)] [Finite I],
Algebra.FormallySmooth R ((i : I) → A i) ↔ ∀ (i : I), Algebra.FormallySmooth R (A i) | true |
Aesop.GoalOrigin.subgoal | Aesop.Tree.Data | Aesop.GoalOrigin | true |
CategoryTheory.prod_id_snd | Mathlib.CategoryTheory.Products.Basic | ∀ (C : Type u₁) [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] (D : Type u₂)
[inst_1 : CategoryTheory.CategoryStruct.{v₂, u₂} D] (X : C × D),
(CategoryTheory.CategoryStruct.id X).2 = CategoryTheory.CategoryStruct.id X.2 | true |
SubMulAction.casesOn | Mathlib.GroupTheory.GroupAction.SubMulAction | {R : Type u} →
{M : Type v} →
[inst : SMul R M] →
{motive : SubMulAction R M → Sort u_1} →
(t : SubMulAction R M) →
((carrier : Set M) →
(smul_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c • x ∈ carrier) →
motive { carrier := carrier, smul_mem' := smul_mem' }) →
... | false |
Lat._sizeOf_1 | Mathlib.Order.Category.Lat | Lat → ℕ | false |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.EmitToString.casesOn | Lean.Compiler.LCNF.EmitC | {α : Type} →
{motive : Lean.Compiler.LCNF.EmitToString✝ α → Sort u} →
(t : Lean.Compiler.LCNF.EmitToString✝ α) →
((toEmitString : α → Lean.Compiler.LCNF.EmitM✝ String) → motive { toEmitString := toEmitString }) → motive t | false |
Nat.Linear.Expr.toPoly.go.eq_3 | Init.Data.Nat.Linear | ∀ (coeff : ℕ) (a b : Nat.Linear.Expr),
Nat.Linear.Expr.toPoly.go coeff (a.add b) = Nat.Linear.Expr.toPoly.go coeff a ∘ Nat.Linear.Expr.toPoly.go coeff b | true |
mem_tangentConeAt_of_openSegment_subset | Mathlib.Analysis.Calculus.TangentCone.Real | ∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousSMul ℝ E]
{s : Set E} {x y : E}, openSegment ℝ x y ⊆ s → y - x ∈ tangentConeAt ℝ s x | true |
Equiv.pprodProd | Mathlib.Logic.Equiv.Prod | {α₁ : Sort u_2} → {β₁ : Sort u_5} → {α₂ : Type u_9} → {β₂ : Type u_10} → α₁ ≃ α₂ → β₁ ≃ β₂ → α₁ ×' β₁ ≃ α₂ × β₂ | true |
Set.decidableMemPow | Mathlib.Algebra.Group.Pointwise.Set.Finite | {α : Type u_2} →
[inst : Monoid α] →
{s : Set α} →
[Fintype α] → [DecidableEq α] → [DecidablePred fun x => x ∈ s] → (n : ℕ) → DecidablePred fun x => x ∈ s ^ n | true |
iteratedFDeriv_comp_add_left | Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | ∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
(n : ℕ) (a x : E), iteratedFDeriv 𝕜 n (fun z => f (a + z)) x = iteratedFDeriv 𝕜 n f (a + x) | true |
Cardinal.lift_iSup_le_sum | Mathlib.SetTheory.Cardinal.Basic | ∀ {ι : Type u} [Small.{v, u} ι] (f : ι → Cardinal.{v}), Cardinal.lift.{u, v} (⨆ i, f i) ≤ Cardinal.sum f | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.readyForRupAdd_ofArray._proof_1_36 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | ∀ {n : ℕ} (arr : Array (Option (Std.Tactic.BVDecide.LRAT.Internal.DefaultClause n)))
(acc : Array Std.Tactic.BVDecide.LRAT.Internal.Assignment) (i : Std.Tactic.BVDecide.LRAT.Internal.PosFin n) (b : Bool)
(c : Std.Tactic.BVDecide.LRAT.Internal.DefaultClause n)
(hsize : (Std.Tactic.BVDecide.LRAT.Internal.DefaultFor... | false |
Int8.reduceBin._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.3529513953._hygCtx._hyg.3 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | Lean.Name → ℕ → (Int8 → Int8 → Int8) → Lean.Expr → Lean.Meta.SimpM Lean.Meta.Simp.DStep | false |
UInt32.rec.eq._@.Mathlib.Util.CompileInductive.3197476844._hygCtx._hyg.394 | Mathlib.Util.CompileInductive | @UInt32.rec = @UInt32.rec✝ | false |
CategoryTheory.FunctorToTypes.binaryCoproductEquiv._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes | ∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] (F G : CategoryTheory.Functor C (Type u_1)) (a : C)
(x : F.obj a ⊕ G.obj a),
(fun z => (CategoryTheory.FunctorToTypes.binaryCoproductIso F G).hom.app a z)
((fun z => (CategoryTheory.FunctorToTypes.binaryCoproductIso F G).inv.app a z) x) =
x | false |
Module.Basis.orientation_map | Mathlib.LinearAlgebra.Orientation | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
{N : Type u_3} [inst_3 : AddCommGroup M] [inst_4 : AddCommGroup N] [inst_5 : Module R M] [inst_6 : Module R N]
{ι : Type u_4} [inst_7 : Fintype ι] [inst_8 : DecidableEq ι] (e : Module.Basis ι R M) (f : M ≃... | true |
AddSubmonoid.topEquiv_toAddMonoidHom | Mathlib.Algebra.Group.Submonoid.Operations | ∀ {M : Type u_5} [inst : AddZeroClass M], ↑AddSubmonoid.topEquiv = ⊤.subtype | true |
Euclidean.nhds_basis_closedBall | Mathlib.Analysis.InnerProductSpace.EuclideanDist | ∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E] [inst_2 : IsTopologicalAddGroup E]
[inst_3 : T2Space E] [inst_4 : Module ℝ E] [inst_5 : ContinuousSMul ℝ E] [inst_6 : FiniteDimensional ℝ E] {x : E},
(nhds x).HasBasis (fun r => 0 < r) (Euclidean.closedBall x) | true |
UInt8.toFin_ofNat | Init.Data.UInt.Lemmas | ∀ (n : ℕ), (OfNat.ofNat n).toFin = OfNat.ofNat n | true |
ContinuousMap.coeFnAlgHom_apply | Mathlib.Topology.ContinuousMap.Algebra | ∀ {α : Type u_1} [inst : TopologicalSpace α] (R : Type u_2) [inst_1 : CommSemiring R] {A : Type u_3}
[inst_2 : TopologicalSpace A] [inst_3 : Semiring A] [inst_4 : Algebra R A] [inst_5 : IsTopologicalSemiring A]
(f : C(α, A)) (a : α), (ContinuousMap.coeFnAlgHom R) f a = f a | true |
_private.Init.Data.Nat.Lemmas.0.Nat.exists_lt_succ_right'._proof_1_3 | Init.Data.Nat.Lemmas | ∀ {n : ℕ}, ∀ m < n, ¬(m < n ∨ m = n) → False | false |
_private.Lean.Compiler.LCNF.ToLCNF.0.Lean.Compiler.LCNF.ToLCNF.seqToCode.go.match_1.eq_5 | Lean.Compiler.LCNF.ToLCNF | ∀ (motive : Lean.Compiler.LCNF.ToLCNF.Element → Sort u_1)
(auxParam : Lean.Compiler.LCNF.Param Lean.Compiler.LCNF.Purity.pure)
(h_1 :
(decl : Lean.Compiler.LCNF.LetDecl Lean.Compiler.LCNF.Purity.pure) →
motive (Lean.Compiler.LCNF.ToLCNF.Element.let decl))
(h_2 :
(decl : Lean.Compiler.LCNF.FunDecl Le... | true |
ONote.toString._unsafe_rec | Mathlib.SetTheory.Ordinal.Notation | ONote → String | false |
WithCStarModule.prod_inner | Mathlib.Analysis.CStarAlgebra.Module.Constructions | ∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] {E : Type u_2} {F : Type u_3}
[inst_2 : NormedAddCommGroup E] [inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : NormedAddCommGroup F]
[inst_6 : Module ℂ F] [inst_7 : SMul A F] [inst_8 : CStarModule A E] [inst_9 : CStarModule A F]
[inst_... | true |
_private.Mathlib.Analysis.Calculus.Deriv.Inverse.0.HasDerivWithinAt.eventually_ne._simp_1_3 | Mathlib.Analysis.Calculus.Deriv.Inverse | ∀ {α : Type u_2} [inst : Zero α] [inst_1 : OfNat α 3] [NeZero 3], (3 = 0) = False | false |
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.X_u₁_spec | Mathlib.NumberTheory.FLT.Three | ∀ {K : Type u_1} [inst : Field K] {ζ : K} {hζ : IsPrimitiveRoot ζ 3} (S : FermatLastTheoremForThreeGen.Solution✝ hζ)
[inst_1 : NumberField K] [inst_2 : IsCyclotomicExtension {3} ℚ K],
FermatLastTheoremForThreeGen.Solution.X✝ S ^ 3 * ↑(FermatLastTheoremForThreeGen.Solution.u₁✝ S) =
FermatLastTheoremForThreeGen.S... | true |
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