name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Init.Data.ByteArray.Lemmas.0.ByteArray.append_eq_append_iff_of_size_eq_left._simp_1_1 | Init.Data.ByteArray.Lemmas | ∀ {x y : ByteArray}, (x = y) = (x.data = y.data) | false |
Lean.instHashableFVarId.hash | Lean.Expr | Lean.FVarId → UInt64 | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.0.BitVec.reduceUnary.match_1 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | (motive : Option BitVec.Literal → Sort u_1) →
(__discr : Option BitVec.Literal) →
((v : BitVec.Literal) → motive (some v)) → ((x : Option BitVec.Literal) → motive x) → motive __discr | false |
isStrongAntichain_insert | Mathlib.Order.Antichain | ∀ {α : Type u_1} {r : α → α → Prop} {s : Set α} {a : α},
IsStrongAntichain r (insert a s) ↔ IsStrongAntichain r s ∧ ∀ ⦃b : α⦄, b ∈ s → a ≠ b → ∀ (c : α), ¬r a c ∨ ¬r b c | true |
instCoeLieSubalgebraSubmodule | Mathlib.Algebra.Lie.Subalgebra | (R : Type u) →
(L : Type v) →
[inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → Coe (LieSubalgebra R L) (Submodule R L) | true |
AlgebraicGeometry.PresheafedSpace.GlueData._sizeOf_inst | Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing | (C : Type u) →
{inst : CategoryTheory.Category.{v, u} C} → [SizeOf C] → SizeOf (AlgebraicGeometry.PresheafedSpace.GlueData C) | false |
_private.Mathlib.CategoryTheory.Functor.Category.0.CategoryTheory.flipFunctor._proof_5 | Mathlib.CategoryTheory.Functor.Category | ∀ (C : Type u_4) [inst : CategoryTheory.Category.{u_3, u_4} C] (D : Type u_6)
[inst_1 : CategoryTheory.Category.{u_5, u_6} D] (E : Type u_2) [inst_2 : CategoryTheory.Category.{u_1, u_2} E]
(X : CategoryTheory.Functor C (CategoryTheory.Functor D E)) (x : D) (x_1 : C),
({ app := fun Y => { app := fun X_1 => ((Categ... | false |
_private.Mathlib.Data.Finset.Powerset.0.Finset.powersetCard_map._simp_1_3 | Mathlib.Data.Finset.Powerset | ∀ {α : Type u_1} {β : Type u_2} {f : α ↪ β} {s₁ s₂ : Finset α}, (Finset.map f s₁ ⊆ Finset.map f s₂) = (s₁ ⊆ s₂) | false |
_private.Init.Data.List.Lemmas.0.List.flatten.match_1.eq_2 | Init.Data.List.Lemmas | ∀ {α : Type u_1} (motive : List (List α) → Sort u_2) (l : List α) (L : List (List α)) (h_1 : Unit → motive [])
(h_2 : (l : List α) → (L : List (List α)) → motive (l :: L)),
(match l :: L with
| [] => h_1 ()
| l :: L => h_2 l L) =
h_2 l L | true |
equicontinuousAt_iff_range | Mathlib.Topology.UniformSpace.Equicontinuity | ∀ {ι : Type u_1} {X : Type u_3} {α : Type u_6} [tX : TopologicalSpace X] [uα : UniformSpace α] {F : ι → X → α} {x₀ : X},
EquicontinuousAt F x₀ ↔ EquicontinuousAt Subtype.val x₀ | true |
AddCommGroup.modEq_iff_natModEq | Mathlib.Data.Nat.ModEq | ∀ {a b n : ℕ}, a ≡ b [PMOD n] ↔ a ≡ b [MOD n] | true |
iteratedDerivWithin_fun_sum | Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {ι : Type u_7} {n : ℕ} {x : 𝕜} {f : ι → 𝕜 → F} {I : Finset ι} {s : Set 𝕜},
x ∈ s →
UniqueDiffOn 𝕜 s →
(∀ i ∈ I, ContDiffWithinAt 𝕜 (↑n) (f i) s x) →
iteratedDerivWi... | true |
Std.DHashMap.getD_modify | 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 k' : α}
{fallback : β k'} {f : β k → β k},
(m.modify k f).getD k' fallback =
if heq : (k == k') = true then (Option.map (cast ⋯) (Option.map f (m.get? k))).getD fallback else m.getD k' fallback | true |
AddSubgroup.isComplement_iff_bijective | Mathlib.GroupTheory.Complement | ∀ {G : Type u_1} [inst : AddGroup G] {S : Type u_2} [inst_1 : SetLike S G] (s t : S),
AddSubgroup.IsComplement ↑s ↑t ↔ Function.Bijective fun x => ↑x.1 + ↑x.2 | true |
instToStringFormat | Init.Data.ToString.Basic | ToString Std.Format | true |
Vector.mem_append_right | Init.Data.Vector.Lemmas | ∀ {α : Type u_1} {n m : ℕ} {a : α} (xs : Vector α n) {ys : Vector α m}, a ∈ ys → a ∈ xs ++ ys | true |
NonUnitalSubsemiring.closure_mono | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | ∀ {R : Type u} [inst : NonUnitalNonAssocSemiring R] ⦃s t : Set R⦄,
s ⊆ t → NonUnitalSubsemiring.closure s ≤ NonUnitalSubsemiring.closure t | true |
Aesop.GoalKind.recOn | Aesop.Stats.Basic | {motive : Aesop.GoalKind → Sort u} →
(t : Aesop.GoalKind) → motive Aesop.GoalKind.preNorm → motive Aesop.GoalKind.postNorm → motive t | false |
FreeAddGroup.Red.negRev | Mathlib.GroupTheory.FreeGroup.Basic | ∀ {α : Type u} {L₁ L₂ : List (α × Bool)},
FreeAddGroup.Red L₁ L₂ → FreeAddGroup.Red (FreeAddGroup.negRev L₁) (FreeAddGroup.negRev L₂) | true |
CategoryTheory.BinaryCofan.isVanKampen_iff | Mathlib.CategoryTheory.Limits.VanKampen | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (c : CategoryTheory.Limits.BinaryCofan X Y),
CategoryTheory.IsVanKampenColimit c ↔
∀ {X' Y' : C} (c' : CategoryTheory.Limits.BinaryCofan X' Y') (αX : X' ⟶ X) (αY : Y' ⟶ Y) (f : c'.pt ⟶ c.pt),
CategoryTheory.CategoryStruct.comp αX c.inl = Cat... | true |
_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.summable_weierstrassPExceptSummand._simp_1_7 | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | ∀ {α : Type u_2} [inst : Zero α] [inst_1 : OfNat α 3] [NeZero 3], (3 = 0) = False | false |
_private.Batteries.Data.String.Lemmas.0.String.utf8GetAux_of_valid._simp_1_3 | Batteries.Data.String.Lemmas | ∀ {x y : String.Pos.Raw}, (x = y) = (x.byteIdx = y.byteIdx) | false |
Std.ExtTreeMap.getD_eq_fallback_of_contains_eq_false | Std.Data.ExtTreeMap.Lemmas | ∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t : Std.ExtTreeMap α β cmp} [inst : Std.TransCmp cmp] {a : α}
{fallback : β}, t.contains a = false → t.getD a fallback = fallback | true |
_private.Mathlib.CategoryTheory.Limits.Shapes.Images.0.CategoryTheory.Limits.IsImage.ofArrowIso._simp_2 | Mathlib.CategoryTheory.Limits.Shapes.Images | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (α : Y ⟶ X) [inst_1 : CategoryTheory.IsIso α]
{f : Z ⟶ X} {g : Z ⟶ Y},
(CategoryTheory.CategoryStruct.comp f (CategoryTheory.inv α) = g) = (f = CategoryTheory.CategoryStruct.comp g α) | false |
Polynomial.supNorm_eq_zero_iff | Mathlib.Analysis.Polynomial.Norm | ∀ {A : Type u_1} [inst : NormedRing A] (p : Polynomial A), p.supNorm = 0 ↔ p = 0 | true |
UpperSet.instAddAction._proof_1 | Mathlib.Algebra.Order.UpperLower | ∀ {α : Type u_1} [inst : Preorder α], Function.Injective SetLike.coe | false |
CategoryTheory.GrothendieckTopology.toPlus_comp_plusCompIso_inv | Mathlib.CategoryTheory.Sites.CompatiblePlus | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u_1}
[inst_1 : CategoryTheory.Category.{v_1, u_1} D] {E : Type u_2} [inst_2 : CategoryTheory.Category.{v_2, u_2} E]
(F : CategoryTheory.Functor D E)
[inst_3 :
∀ (J : CategoryTheory.Limits.Multicospan... | true |
Int.tdiv.eq_4 | Init.Data.Int.DivMod.Lemmas | ∀ (m n : ℕ), (Int.negSucc m).tdiv (Int.negSucc n) = Int.ofNat (m.succ / n.succ) | true |
closedBall_rpow_sub_one_eq_empty_aux | Mathlib.Analysis.SpecialFunctions.JapaneseBracket | ∀ (E : Type u_1) [inst : NormedAddCommGroup E] {r t : ℝ}, 0 < r → 1 < t → Metric.closedBall 0 (t ^ (-r⁻¹) - 1) = ∅ | true |
Vector.mapFinIdx._proof_1 | Init.Data.Vector.Basic | ∀ {α : Type u_1} {n : ℕ} (xs : Vector α n), ∀ i < xs.toArray.size, i < n | false |
_private.Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Basic.0.IsCovariantDerivativeOn.difference._proof_7 | Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Basic | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_4} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_5}
[inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {V : M → Type u_2} [inst_6 : (x : M) → ... | false |
_private.Mathlib.Order.Filter.ENNReal.0.NNReal.toReal_liminf._simp_1_8 | Mathlib.Order.Filter.ENNReal | ∀ {p : NNReal → Prop}, (∀ (x : NNReal), p x) = ∀ (x : ℝ) (hx : 0 ≤ x), p ⟨x, hx⟩ | false |
Array.eraseIdx_insertIdx_self | Init.Data.Array.InsertIdx | ∀ {α : Type u} {a : α} {i : ℕ} {xs : Array α} (h : i ≤ xs.size), (xs.insertIdx i a h).eraseIdx i ⋯ = xs | true |
OrderDual.instDivisionRing | Mathlib.Algebra.Field.Basic | {K : Type u_1} → [h : DivisionRing K] → DivisionRing Kᵒᵈ | true |
Std.DTreeMap.Internal.Impl.Const.get?_insertManyIfNewUnit_list | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {instOrd : Ord α} {t : Std.DTreeMap.Internal.Impl α fun x => Unit} [Std.TransOrd α] [inst : BEq α]
[Std.LawfulBEqOrd α] (h : t.WF) {l : List α} {k : α},
Std.DTreeMap.Internal.Impl.Const.get? (↑(Std.DTreeMap.Internal.Impl.Const.insertManyIfNewUnit t l ⋯)) k =
if k ∈ t ∨ l.contains k = true then so... | true |
Lean.Compiler.LCNF.Simp.DiscrM.Context.mk.sizeOf_spec | Lean.Compiler.LCNF.Simp.DiscrM | ∀ (discrCtorMap : Lean.FVarIdMap Lean.Compiler.LCNF.Simp.CtorInfo) (ctorDiscrMap : Lean.PersistentExprMap Lean.FVarId),
sizeOf { discrCtorMap := discrCtorMap, ctorDiscrMap := ctorDiscrMap } = 1 + sizeOf discrCtorMap + sizeOf ctorDiscrMap | true |
MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | Mathlib.MeasureTheory.Measure.Restrict | ∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {t : Set ↑s},
MeasureTheory.NullMeasurableSet s μ → MeasurableSet t → MeasureTheory.NullMeasurableSet (Subtype.val '' t) μ | true |
Ideal.uniqueUnits | Mathlib.RingTheory.Ideal.Operations | {R : Type u} → [inst : CommSemiring R] → Unique (Ideal R)ˣ | true |
Complex.range_sin | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | Set.range Complex.sin = Set.univ | true |
instAssociativeMinOnOfIsLinearPreorder | Init.Data.Order.MinMaxOn | ∀ {β : Type u_1} {α : Sort u_2} [inst : LE β] [inst_1 : DecidableLE β] [Std.IsLinearPreorder β] {f : α → β},
Std.Associative (minOn f) | true |
AddOpposite.instDecidableEq | Mathlib.Algebra.Opposites | {α : Type u_1} → [DecidableEq α] → DecidableEq αᵃᵒᵖ | true |
Lean.Grind.AC.Context.vars | Init.Grind.AC | {α : Sort u} → Lean.Grind.AC.Context α → Lean.RArray (PLift α) | true |
ContinuousMap.instRing._proof_8 | Mathlib.Topology.ContinuousMap.Algebra | ∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : Ring β]
[inst_3 : IsTopologicalRing β] (f g : C(α, β)), ⇑(f + g) = ⇑f + ⇑g | false |
CategoryTheory.InjectiveResolution.extEquivCohomologyClass._proof_6 | Mathlib.CategoryTheory.Abelian.Injective.Ext | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C],
(HomologicalComplex.quasiIso C (ComplexShape.up ℤ)).IsCompatibleWithShift ℤ | false |
Filter.EventuallyEq.mapClusterPt_iff | Mathlib.Topology.ClusterPt | ∀ {X : Type u} [inst : TopologicalSpace X] {α : Type u_1} {F : Filter α} {u : α → X} {x : X} {v : α → X},
u =ᶠ[F] v → (MapClusterPt x F u ↔ MapClusterPt x F v) | true |
sbtw_const_vsub_iff | Mathlib.Analysis.Convex.Between | ∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
[inst_3 : Module R V] [inst_4 : AddTorsor V P] {x y z : P} (p : P), Sbtw R (p -ᵥ x) (p -ᵥ y) (p -ᵥ z) ↔ Sbtw R x y z | true |
CategoryTheory.sum.inrCompInrCompInverseAssociator_hom_app_down | Mathlib.CategoryTheory.Sums.Associator | ∀ (C : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} C] (D : Type u₂) [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(E : Type u₃) [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (X : E),
((CategoryTheory.sum.inrCompInrCompInverseAssociator C D E).hom.app X).down =
CategoryTheory.CategoryStruct.comp (CategoryT... | true |
Lean.Parser.Tactic.Grind.finishTrace | Init.Grind.Interactive | Lean.ParserDescr | true |
_private.Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm.0.PiTensorProduct.wrapped._proof_1._@.Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm.2741663271._hygCtx._hyg.2 | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | @PiTensorProduct.definition✝ = @PiTensorProduct.definition✝ | false |
CategoryTheory.Limits.pasteVertIsPushout | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{Y₃ Y₂ Y₁ X₃ : C} →
{g₂ : Y₃ ⟶ Y₂} →
{g₁ : Y₂ ⟶ Y₁} →
{i₃ : Y₃ ⟶ X₃} →
{t₁ : CategoryTheory.Limits.PushoutCocone g₂ i₃} →
{i₂ : Y₂ ⟶ t₁.pt} →
{t₂ : CategoryTheory.Limits.PushoutCocone g₁ i₂... | true |
CategoryTheory.MonoidalClosed.curry.eq_1 | Mathlib.CategoryTheory.LocallyCartesianClosed.Sections | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {A X Y : C}
[inst_2 : CategoryTheory.Closed A],
CategoryTheory.MonoidalClosed.curry = ⇑((CategoryTheory.ihom.adjunction A).homEquiv Y X) | true |
Lean.Server.Completion.EligibleDecl.recOn | Lean.Server.Completion.EligibleHeaderDecls | {motive : Lean.Server.Completion.EligibleDecl → Sort u} →
(t : Lean.Server.Completion.EligibleDecl) →
((info : Lean.ConstantInfo) →
(kind : Lean.MetaM Lean.Lsp.CompletionItemKind) →
(tags : Lean.MetaM (Array Lean.Lsp.CompletionItemTag)) →
motive { info := info, kind := kind, tags := ... | false |
Vector.zip_replicate | Init.Data.Vector.Zip | ∀ {α : Type u_1} {β : Type u_2} {a : α} {b : β} {n : ℕ},
(Vector.replicate n a).zip (Vector.replicate n b) = Vector.replicate n (a, b) | true |
CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd._proof_14 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
(X Y : C) ⦃X_1 Y_1 : CategoryTheory.Over Y⦄ (f : X_1 ⟶ Y_1),
CategoryTheory.CategoryStruct.comp
(({ obj := fun Z => CategoryTheory.Over.mk (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X Z... | false |
_private.Lean.Data.Lsp.LanguageFeatures.0.Lean.Lsp.instBEqInsertReplaceEdit.beq.match_1 | Lean.Data.Lsp.LanguageFeatures | (motive : Lean.Lsp.InsertReplaceEdit → Lean.Lsp.InsertReplaceEdit → Sort u_1) →
(x x_1 : Lean.Lsp.InsertReplaceEdit) →
((a : String) →
(a_1 a_2 : Lean.Lsp.Range) →
(b : String) →
(b_1 b_2 : Lean.Lsp.Range) →
motive { newText := a, insert := a_1, replace := a_2 } { newTe... | false |
_private.Mathlib.Geometry.Euclidean.Angle.Incenter.0.Affine.Triangle.oangle_incenter_eq._proof_1_1 | Mathlib.Geometry.Euclidean.Angle.Incenter | NeZero (1 + 1) | false |
ContinuousMap.HomotopicRel.equivalence | Mathlib.Topology.Homotopy.Basic | ∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {S : Set X},
Equivalence fun f g => f.HomotopicRel g S | true |
CategoryTheory.Abelian.coimageStrongEpiMonoFactorisation_I | Mathlib.CategoryTheory.Abelian.Basic | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {P Q : C} (f : P ⟶ Q),
(CategoryTheory.Abelian.coimageStrongEpiMonoFactorisation f).I = CategoryTheory.Abelian.coimage f | true |
_private.Mathlib.RingTheory.Congruence.Hom.0.RingCon.correspondence._simp_5 | Mathlib.RingTheory.Congruence.Hom | ∀ {R : Type u_3} [inst : Add R] [inst_1 : Mul R] {c d : RingCon R}, (c ≤ d) = ∀ {x y : R}, c x y → d x y | false |
SimpleGraph.Subgraph.IsMatching | Mathlib.Combinatorics.SimpleGraph.Matching | {V : Type u_1} → {G : SimpleGraph V} → G.Subgraph → Prop | true |
Finset.le_truncatedSup | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | ∀ {α : Type u_1} [inst : SemilatticeSup α] {s : Finset α} {a : α} [inst_1 : DecidableLE α] [inst_2 : OrderTop α],
a ≤ s.truncatedSup a | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic.0.WeierstrassCurve.Projective.nonsingular_some._simp_1_8 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | ∀ {a b c : Prop}, (a ∧ b ↔ a ∧ c) = (a → (b ↔ c)) | false |
contDiffPointwiseHolderAt_iff | Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | ∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] (k : ℕ) (α : ↑unitInterval) (f : E → F) (a : E),
ContDiffPointwiseHolderAt k α f a ↔
ContDiffAt ℝ (↑k) f a ∧ (fun x => iteratedFDeriv ℝ k f x - iteratedFDeriv ℝ k f... | true |
_private.Init.Data.String.Lemmas.Order.0.String.Slice.Pos.next_eq_iff.match_1_1 | Init.Data.String.Lemmas.Order | ∀ {s : String.Slice} {p q : s.Pos} (motive : (p < q ∧ ∀ (q' : s.Pos), p < q' → q ≤ q') → Prop)
(x : p < q ∧ ∀ (q' : s.Pos), p < q' → q ≤ q'),
(∀ (h₁ : p < q) (h₂ : ∀ (q' : s.Pos), p < q' → q ≤ q'), motive ⋯) → motive x | false |
Set.singleton_union | Mathlib.Data.Set.Insert | ∀ {α : Type u_1} {s : Set α} {a : α}, {a} ∪ s = insert a s | true |
Trunc.nonempty | Mathlib.Data.Quot | ∀ {α : Sort u_1} (q : Trunc α), Nonempty α | true |
_private.Mathlib.CategoryTheory.Monoidal.Mon_.0.CategoryTheory.MonObj.ofIso._simp_1 | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {C : Type u} {𝒞 : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.MonoidalCategory C] {X₁ Y₁ X₂ Y₂ : C}
(f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) {Z : C} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj Y₁ Y₂ ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X₂)
... | false |
_private.Mathlib.Tactic.Linter.FlexibleLinter.0.Mathlib.Linter.Flexible.TacticData.mctxBefore | Mathlib.Tactic.Linter.FlexibleLinter | Mathlib.Linter.Flexible.TacticData✝ → Lean.MetavarContext | true |
_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.addIncBeforeAux | Lean.Compiler.LCNF.ExplicitRC | Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Purity.impure) →
(ℕ → Bool) →
Lean.Compiler.LCNF.Code Lean.Compiler.LCNF.Purity.impure →
Lean.Compiler.LCNF.RcM✝ (Lean.Compiler.LCNF.Code Lean.Compiler.LCNF.Purity.impure) | true |
ProofWidgets.instToJsonRpcEncodablePacket.toJson._@.ProofWidgets.Data.Html.2463204861._hygCtx._hyg.58 | ProofWidgets.Data.Html | ProofWidgets.RpcEncodablePacket✝ → Lean.Json | false |
LinearGrowth.linearGrowthInf_iInf | Mathlib.Analysis.Asymptotics.LinearGrowth | ∀ {ι : Type u_1} [Finite ι] (u : ι → ℕ → EReal),
LinearGrowth.linearGrowthInf (⨅ i, u i) = ⨅ i, LinearGrowth.linearGrowthInf (u i) | true |
Array.instOrientedOrd | Init.Data.Order.Ord | ∀ {α : Type u_1} [inst : Ord α] [Std.OrientedOrd α], Std.OrientedOrd (Array α) | true |
_private.Lean.Meta.CongrTheorems.0.Lean.Meta.mkHCongrWithArity.mkProof.match_1 | Lean.Meta.CongrTheorems | (motive : Option (Lean.Expr × Lean.Expr × Lean.Expr × Lean.Expr) → Sort u_1) →
(x : Option (Lean.Expr × Lean.Expr × Lean.Expr × Lean.Expr)) →
((fst lhs fst_1 snd : Lean.Expr) → motive (some (fst, lhs, fst_1, snd))) →
((x : Option (Lean.Expr × Lean.Expr × Lean.Expr × Lean.Expr)) → motive x) → motive x | false |
Even.pow_nonneg | Mathlib.Algebra.Order.Ring.Basic | ∀ {R : Type u_3} [inst : Semiring R] [inst_1 : LinearOrder R] [IsOrderedRing R] [ExistsAddOfLE R] {n : ℕ},
Even n → ∀ (a : R), 0 ≤ a ^ n | true |
Lean.Elab.Command.elabInductiveCommand._regBuiltin.Lean.Elab.Command.elabInductiveCommand_3 | Lean.Elab.Inductive | IO Unit | false |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_66 | Batteries.Data.List.Lemmas | ∀ {α : Type u_1} {x : α} [inst : BEq α] (head : α) (tail : List α) {n s : ℕ}
{h : n < (List.idxsOf x (head :: tail) s).length},
(head == x) = true → (List.idxsOf x (head :: tail) s)[0] - s < (head :: tail).length | false |
selfAdjoint.instNNRatCast._proof_1 | Mathlib.Algebra.Star.SelfAdjoint | ∀ {R : Type u_1} [inst : Field R] [inst_1 : StarRing R] (q : ℚ≥0), IsSelfAdjoint ↑q | false |
Array.count_eq_zero_of_not_mem | Init.Data.Array.Count | ∀ {α : Type u_1} [inst : BEq α] [LawfulBEq α] {a : α} {xs : Array α}, a ∉ xs → Array.count a xs = 0 | true |
Set.countable_iUnion_iff._simp_1 | Mathlib.Data.Set.Countable | ∀ {α : Type u} {ι : Sort x} [Countable ι] {t : ι → Set α}, (⋃ i, t i).Countable = ∀ (i : ι), (t i).Countable | false |
MeasureTheory.Lp._proof_4 | Mathlib.MeasureTheory.Function.LpSpace.Basic | ∀ (E : Type u_1) [inst : NormedAddCommGroup E], IsTopologicalAddGroup E | false |
Set.Ioo_sub_one_left_eq_Ioc | Mathlib.Algebra.Order.Interval.Set.SuccPred | ∀ {α : Type u_2} [inst : LinearOrder α] [inst_1 : One α] [inst_2 : Sub α] [PredSubOrder α] [NoMinOrder α] (a b : α),
Set.Ioo (a - 1) b = Set.Ico a b | true |
LieModule.nontrivial_lowerCentralSeriesLast | Mathlib.Algebra.Lie.Nilpotent | ∀ (R : Type u) (L : Type v) (M : Type w) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [LieModule R L M] [Nontrivial M]
[LieModule.IsNilpotent L M], Nontrivial ↥(LieModule.lowerCentralSeriesLast R L M) | true |
FractionalIdeal.map_coeIdeal | Mathlib.RingTheory.FractionalIdeal.Operations | ∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
{P' : Type u_3} [inst_3 : CommRing P'] [inst_4 : Algebra R P'] (g : P →ₐ[R] P') (I : Ideal R),
FractionalIdeal.map g ↑I = ↑I | true |
Std.DHashMap.Internal.Raw₀.get!ₘ_eq_getValueCast! | Std.Data.DHashMap.Internal.WF | ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] [inst_2 : LawfulBEq α]
{m : Std.DHashMap.Internal.Raw₀ α β},
Std.DHashMap.Internal.Raw.WFImp ↑m →
∀ {a : α} [inst_3 : Inhabited (β a)],
m.get!ₘ a = Std.Internal.List.getValueCast! a (Std.DHashMap.Internal.toListModel (↑m).buckets) | true |
_private.Init.Data.Array.Find.0.Array.of_findIdx?_eq_some.match_1.splitter | Init.Data.Array.Find | {α : Type u_1} →
(motive : Option α → Sort u_2) → (x : Option α) → ((a : α) → motive (some a)) → (Unit → motive none) → motive x | true |
CategoryTheory.Functor.Monoidal.ε_η | Mathlib.CategoryTheory.Monoidal.Functor | ∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} {D : Type u₂}
{inst_2 : CategoryTheory.Category.{v₂, u₂} D} {inst_3 : CategoryTheory.MonoidalCategory D}
(F : CategoryTheory.Functor C D) [self : F.Monoidal],
CategoryTheory.CategoryStruct.comp (CategoryTheory... | true |
FirstOrder.Field.FieldAxiom.toSentence.eq_9 | Mathlib.ModelTheory.Algebra.Field.Basic | FirstOrder.Field.FieldAxiom.existsPairNE.toSentence =
(((FirstOrder.Language.var ∘ Sum.inr) 0).bdEqual ((FirstOrder.Language.var ∘ Sum.inr) 1)).not.ex.ex | true |
SeparationQuotient.t2Space_iff | Mathlib.Topology.Separation.Hausdorff | ∀ {X : Type u_1} [inst : TopologicalSpace X], T2Space (SeparationQuotient X) ↔ R1Space X | true |
BitVec.getLsbD_ofBool | Init.Data.BitVec.Lemmas | ∀ (b : Bool) (i : ℕ), (BitVec.ofBool b).getLsbD i = (decide (i = 0) && b) | true |
Submodule.span_singleton_mul | Mathlib.Algebra.Algebra.Operations | ∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] {x : A}
{p : Submodule R A}, (R ∙ x) * p = x • p | true |
div_self_eq_one₀._simp_1 | Mathlib.Algebra.GroupWithZero.Units.Basic | ∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a : G₀}, (a / a = 1) = (a ≠ 0) | false |
_private.Mathlib.Probability.Independence.Basic.0.ProbabilityTheory.iIndepFun_iff._simp_1_2 | Mathlib.Probability.Independence.Basic | ∀ {Ω : Type u_1} {ι : Type u_2} (m : ι → MeasurableSpace Ω) {_mΩ : MeasurableSpace Ω} (μ : MeasureTheory.Measure Ω),
ProbabilityTheory.iIndep m μ =
∀ (s : Finset ι) {f : ι → Set Ω}, (∀ i ∈ s, MeasurableSet (f i)) → μ (⋂ i ∈ s, f i) = ∏ i ∈ s, μ (f i) | false |
Std.Roo.toList_eq_match_rco | Init.Data.Range.Polymorphic.Lemmas | ∀ {α : Type u} {r : Std.Roo α} [inst : Std.PRange.UpwardEnumerable α] [inst_1 : LT α] [inst_2 : DecidableLT α]
[inst_3 : Std.PRange.LawfulUpwardEnumerable α] [Std.PRange.LawfulUpwardEnumerableLT α]
[inst_5 : Std.Rxo.IsAlwaysFinite α],
r.toList =
match Std.PRange.succ? r.lower with
| none => []
| some ... | true |
Simps.ProjectionData.mk._flat_ctor | Mathlib.Tactic.Simps.Basic | Lean.Name → Lean.Expr → List ℕ → Bool → Bool → Simps.ProjectionData | false |
SchwartzMap.smulRightCLM._proof_1 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | ∀ {E : Type u_1} (F : Type u_2) {G : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace ℝ G]
(L : E →L[ℝ] G →L[ℝ] ℝ) (f g : SchwartzMap E F) (x : E),
(fun f x => (L x).smulRight (f x)) ... | false |
Complex.instCoeReal | Mathlib.Data.Complex.Basic | Coe ℝ ℂ | true |
Std.Iterators.Types.FilterMap.mk.inj | Init.Data.Iterators.Combinators.Monadic.FilterMap | ∀ {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {lift : ⦃α : Type w⦄ → m α → n α}
{f : β → Std.Iterators.PostconditionT n (Option γ)} {inner inner_1 : Std.IterM m β},
{ inner := inner } = { inner := inner_1 } → inner = inner_1 | true |
_private.Lean.Compiler.LCNF.ToLCNF.0.Lean.Compiler.LCNF.ToLCNF.isTypeFormerType.match_1 | Lean.Compiler.LCNF.ToLCNF | (motive : Option Bool → Sort u_1) →
(x : Option Bool) → ((result : Bool) → motive (some result)) → ((x : Option Bool) → motive x) → motive x | false |
Subalgebra.instSubringClass | Mathlib.Algebra.Algebra.Subalgebra.Basic | ∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A],
SubringClass (Subalgebra R A) A | true |
iSupIndep.linearEquiv_symm_apply | Mathlib.LinearAlgebra.DFinsupp | ∀ {ι : Type u_1} {R : Type u_3} {N : Type u_6} [inst : DecidableEq ι] [inst_1 : Ring R] [inst_2 : AddCommGroup N]
[inst_3 : Module R N] {p : ι → Submodule R N} (ind : iSupIndep p) (iSup_top : ⨆ i, p i = ⊤) {i : ι} {x : N}
(h : x ∈ p i), (ind.linearEquiv iSup_top).symm x = fun₀ | i => ⟨x, h⟩ | true |
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