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bool
2 classes
Std.Time.Weekday.noConfusionType
Std.Time.Date.Unit.Weekday
Sort v✝ → Std.Time.Weekday → Std.Time.Weekday → Sort v✝
true
CategoryTheory.Limits.WidePushoutShape.equivalenceOfEquiv._proof_10
Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
∀ {J : Type u_1} (J' : Type u_2) (h : J ≃ J') (X : CategoryTheory.Limits.WidePushoutShape J), CategoryTheory.CategoryStruct.comp ((CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h j)).map ((CategoryTheory.NatIso.ofComponents (fun j => Option.casesOn (motive := fun t => j = t → ((CategoryTheory.Functor.id (CategoryTheory.Limits.WidePushoutShape J)).obj j ≅ ((CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h j)).comp (CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h.invFun j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h.invFun j))).obj j)) j (fun h_1 => ⋯ ▸ CategoryTheory.eqToIso ⋯) (fun val h_1 => ⋯ ▸ CategoryTheory.eqToIso ⋯) ⋯) ⋯).hom.app X)) ((CategoryTheory.NatIso.ofComponents (fun j => Option.casesOn (motive := fun t => j = t → (((CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h.invFun j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h.invFun j)).comp (CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h j))).obj j ≅ (CategoryTheory.Functor.id (CategoryTheory.Limits.WidePushoutShape J')).obj j)) j (fun h_1 => ⋯ ▸ CategoryTheory.eqToIso ⋯) (fun val h_1 => ⋯ ▸ CategoryTheory.eqToIso ⋯) ⋯) ⋯).hom.app ((CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h j)).obj X)) = CategoryTheory.CategoryStruct.id ((CategoryTheory.Limits.WidePushoutShape.wideSpan none (fun j => some (h j)) fun j => CategoryTheory.Limits.WidePushoutShape.Hom.init (h j)).obj X)
false
Finset.HasAntidiagonal.antidiagonal
Mathlib.Algebra.Order.Antidiag.Prod
{A : Type u_1} → {inst : AddMonoid A} → [self : Finset.HasAntidiagonal A] → A → Finset (A × A)
true
Finset.mul_eq_empty._simp_2
Mathlib.Algebra.Group.Pointwise.Finset.Basic
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Mul α] {s t : Finset α}, (s * t = ∅) = (s = ∅ ∨ t = ∅)
false
Std.ExtDTreeMap.get?_diff
Std.Data.ExtDTreeMap.Lemmas
∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.ExtDTreeMap α β cmp} [inst : Std.TransCmp cmp] [inst_1 : Std.LawfulEqCmp cmp] {k : α}, (t₁ \ t₂).get? k = if k ∈ t₂ then none else t₁.get? k
true
Array.foldr_subtype'
Init.Data.Array.Attach
∀ {α : Type u_1} {β : Type u_2} {start : ℕ} {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → β → β} {g : α → β → β} {x : β}, (∀ (x : α) (h : p x) (b : β), f ⟨x, h⟩ b = g x b) → start = xs.size → Array.foldr f x xs start = Array.foldr g x xs.unattach
true
CategoryTheory.Pretriangulated.rotCompInvRot
Mathlib.CategoryTheory.Triangulated.Rotate
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → [inst_1 : CategoryTheory.Preadditive C] → [inst_2 : CategoryTheory.HasShift C ℤ] → [∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] → CategoryTheory.Functor.id (CategoryTheory.Pretriangulated.Triangle C) ≅ (CategoryTheory.Pretriangulated.rotate C).comp (CategoryTheory.Pretriangulated.invRotate C)
true
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.updateCell.match_5.eq_1
Std.Data.DTreeMap.Internal.Model
∀ {α : Type u_1} {β : α → Type u_2} (motive : (l : Std.DTreeMap.Internal.Impl α β) → l.Balanced → Sort u_3) (hl : Std.DTreeMap.Internal.Impl.leaf.Balanced) (h_1 : (hl : Std.DTreeMap.Internal.Impl.leaf.Balanced) → motive Std.DTreeMap.Internal.Impl.leaf hl) (h_2 : (sz : ℕ) → (ky : α) → (y : β ky) → (l r : Std.DTreeMap.Internal.Impl α β) → (hl : (Std.DTreeMap.Internal.Impl.inner sz ky y l r).Balanced) → motive (Std.DTreeMap.Internal.Impl.inner sz ky y l r) hl), (match Std.DTreeMap.Internal.Impl.leaf, hl with | Std.DTreeMap.Internal.Impl.leaf, hl => h_1 hl | Std.DTreeMap.Internal.Impl.inner sz ky y l r, hl => h_2 sz ky y l r hl) = h_1 hl
true
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Besicovitch.TauPackage.color_lt._simp_1_13
Mathlib.MeasureTheory.Covering.Besicovitch
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε : ℝ}, (y ∈ Metric.closedBall x ε) = (dist y x ≤ ε)
false
CategoryTheory.Subobject.pullback_self
Mathlib.CategoryTheory.Subobject.Lattice
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {A B : C} (f : A ⟶ B) [inst_2 : CategoryTheory.Mono f], (CategoryTheory.Subobject.pullback f).obj (CategoryTheory.Subobject.mk f) = ⊤
true
HereditarilyLindelofSpace.isLindelof
Mathlib.Topology.Compactness.Lindelof
∀ {X : Type u} [inst : TopologicalSpace X] [HereditarilyLindelofSpace X] (s : Set X), IsLindelof s
true
Real.cos_sub_cos
Mathlib.Analysis.Complex.Trigonometric
∀ (x y : ℝ), Real.cos x - Real.cos y = -2 * Real.sin ((x + y) / 2) * Real.sin ((x - y) / 2)
true
CStarMatrix.map_apply
Mathlib.Analysis.CStarAlgebra.CStarMatrix
∀ {m : Type u_1} {n : Type u_2} {A : Type u_5} {B : Type u_6} {M : CStarMatrix m n A} {f : A → B} {i : m} {j : n}, M.map f i j = f (M i j)
true
_private.Lean.Widget.UserWidget.0.Lean.Widget.initFn._@.Lean.Widget.UserWidget.1015473889._hygCtx._hyg.2
Lean.Widget.UserWidget
IO Lean.Widget.PanelWidgetsExt✝
false
Lean.Meta.Simp.SimprocOLeanEntry
Lean.Meta.Tactic.Simp.Types
Type
true
_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comapOn_isBase_iff_of_surjOn._simp_1_3
Mathlib.Combinatorics.Matroid.Map
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis' I X = M.IsBasis I (X ∩ M.E)
false
_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.chevalley_mvPolynomialC._simp_1_6
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {p q : Submodule R M} {x : M}, (x ∈ p ⊓ q) = (x ∈ p ∧ x ∈ q)
false
CategoryTheory.plusPlusAdjunction
Mathlib.CategoryTheory.Sites.ConcreteSheafification
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → (J : CategoryTheory.GrothendieckTopology C) → (D : Type w) → [inst_1 : CategoryTheory.Category.{w', w} D] → {FD : D → D → Type u_1} → {CD : D → Type t} → [inst_2 : (X Y : D) → FunLike (FD X Y) (CD X) (CD Y)] → [instCC : CategoryTheory.ConcreteCategory D FD] → [inst_3 : ∀ {X : C} (S : J.Cover X), CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Limits.WalkingMulticospan S.shape) (CategoryTheory.forget D)] → [inst_4 : ∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X), CategoryTheory.Limits.HasMultiequalizer (S.index P)] → [inst_5 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D] → [inst_6 : ∀ (X : C), CategoryTheory.Limits.PreservesColimitsOfShape (J.Cover X)ᵒᵖ (CategoryTheory.forget D)] → [inst_7 : (CategoryTheory.forget D).ReflectsIsomorphisms] → CategoryTheory.plusPlusSheaf J D ⊣ CategoryTheory.sheafToPresheaf J D
true
Lean.Expr.letE
Lean.Expr
Lean.Name → Lean.Expr → Lean.Expr → Lean.Expr → Bool → Lean.Expr
true
Std.DTreeMap.Internal.Impl.ExplorationStep.gt.inj
Std.Data.DTreeMap.Internal.Model
∀ {α : Type u} {β : α → Type v} {inst : Ord α} {k : α → Ordering} {a : List ((a : α) × β a)} {a_1 : α} {a_2 : k a_1 = Ordering.gt} {a_3 : β a_1} {a_4 : List ((a : α) × β a)} {a_5 : α} {a_6 : k a_5 = Ordering.gt} {a_7 : β a_5}, Std.DTreeMap.Internal.Impl.ExplorationStep.gt a a_1 a_2 a_3 = Std.DTreeMap.Internal.Impl.ExplorationStep.gt a_4 a_5 a_6 a_7 → a = a_4 ∧ a_1 = a_5 ∧ a_3 ≍ a_7
true
Set.mapsTo_sUnion
Mathlib.Data.Set.Lattice.Image
∀ {α : Type u_1} {β : Type u_2} {S : Set (Set α)} {t : Set β} {f : α → β}, Set.MapsTo f (⋃₀ S) t ↔ ∀ s ∈ S, Set.MapsTo f s t
true
SubAddAction.ofStabilizer.addConjMap_comp
Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer
∀ {G : Type u_1} [inst : AddGroup G] {α : Type u_2} [inst_1 : AddAction G α] {g h k : G} {a b c : α} (hg : b = g +ᵥ a) (hh : c = h +ᵥ b) (hk : c = k +ᵥ a) (H : k = h + g), (SubAddAction.ofStabilizer.conjMap hh).comp (SubAddAction.ofStabilizer.conjMap hg) = SubAddAction.ofStabilizer.conjMap hk
true
_private.Init.Data.UInt.Bitwise.0.USize.toUInt8_shiftLeft._simp_1_1
Init.Data.UInt.Bitwise
∀ {a b : USize}, (a < b) = (a.toNat < b.toNat)
false
Lean.Grind.Ring.toIntModule
Init.Grind.Ring.Basic
{α : Type u} → [I : Lean.Grind.Ring α] → Lean.Grind.IntModule α
true
RingCat.Colimits.ColimitType.AddGroup._proof_2
Mathlib.Algebra.Category.Ring.Colimits
∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J RingCat) (n : ℕ) (x : RingCat.Colimits.ColimitType F), nsmulRec (n + 1) x = nsmulRec n x + x
false
SpecialLinearGroup.baseChange._proof_3
Mathlib.LinearAlgebra.SpecialLinearGroup
∀ {R : Type u_3} {V : Type u_1} [inst : CommRing R] [inst_1 : AddCommGroup V] [inst_2 : Module R V] {S : Type u_2} [inst_3 : CommRing S] [inst_4 : Algebra R S] [inst_5 : Module.Free R V] [inst_6 : Module.Finite R V] (x y : SpecialLinearGroup R V), ↑⟨LinearEquiv.baseChange R S V V ↑(x * y), ⋯⟩ = ↑(⟨LinearEquiv.baseChange R S V V ↑x, ⋯⟩ * ⟨LinearEquiv.baseChange R S V V ↑y, ⋯⟩)
false
CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDesc.congr_simp
Mathlib.CategoryTheory.GradedObject.Trifunctor
∀ {C₁ : Type u_1} {C₂ : Type u_2} {C₃ : Type u_3} {C₄ : Type u_4} {C₁₂ : Type u_5} [inst : CategoryTheory.Category.{v_1, u_1} C₁] [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_3, u_3} C₃] [inst_3 : CategoryTheory.Category.{v_4, u_4} C₄] [inst_4 : CategoryTheory.Category.{v_5, u_5} C₁₂] {F₁₂ : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₁₂)} {G : CategoryTheory.Functor C₁₂ (CategoryTheory.Functor C₃ C₄)} {I₁ : Type u_7} {I₂ : Type u_8} {I₃ : Type u_9} {J : Type u_10} {r : I₁ × I₂ × I₃ → J} {ρ₁₂ : CategoryTheory.GradedObject.BifunctorComp₁₂IndexData r} {X₁ : CategoryTheory.GradedObject I₁ C₁} {X₂ : CategoryTheory.GradedObject I₂ C₂} {X₃ : CategoryTheory.GradedObject I₃ C₃} [inst_5 : (((CategoryTheory.GradedObject.mapBifunctor F₁₂ I₁ I₂).obj X₁).obj X₂).HasMap ρ₁₂.p] [inst_6 : (((CategoryTheory.GradedObject.mapBifunctor G ρ₁₂.I₁₂ I₃).obj (CategoryTheory.GradedObject.mapBifunctorMapObj F₁₂ ρ₁₂.p X₁ X₂)).obj X₃).HasMap ρ₁₂.q] [H : CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj F₁₂ G ρ₁₂ X₁ X₂ X₃] {j : J} {A : C₄} (f f_1 : (i₁ : I₁) → (i₂ : I₂) → (i₃ : I₃) → r (i₁, i₂, i₃) = j → ((G.obj ((F₁₂.obj (X₁ i₁)).obj (X₂ i₂))).obj (X₃ i₃) ⟶ A)), f = f_1 → CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDesc f = CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDesc f_1
true
Lean.Meta.AbstractMVars.State.recOn
Lean.Meta.AbstractMVars
{motive : Lean.Meta.AbstractMVars.State → Sort u} → (t : Lean.Meta.AbstractMVars.State) → ((ngen : Lean.NameGenerator) → (lctx : Lean.LocalContext) → (mctx : Lean.MetavarContext) → (nextParamIdx : ℕ) → (paramNames : Array Lean.Name) → (fvars mvars : Array Lean.Expr) → (lmap : Std.HashMap Lean.LMVarId Lean.Level) → (emap : Std.HashMap Lean.MVarId Lean.Expr) → (abstractLevels : Bool) → motive { ngen := ngen, lctx := lctx, mctx := mctx, nextParamIdx := nextParamIdx, paramNames := paramNames, fvars := fvars, mvars := mvars, lmap := lmap, emap := emap, abstractLevels := abstractLevels }) → motive t
false
Seminorm.continuous_iff_continuous_comp
Mathlib.Analysis.LocallyConvex.WithSeminorms
∀ {𝕝 : Type u_4} {𝕝₂ : Type u_5} {E : Type u_6} {F : Type u_7} {ι' : Type u_10} [inst : AddCommGroup E] [inst_1 : NormedField 𝕝] [inst_2 : Module 𝕝 E] [inst_3 : AddCommGroup F] [inst_4 : NormedField 𝕝₂] [inst_5 : Module 𝕝₂ F] {τ₁₂ : 𝕝 →+* 𝕝₂} [inst_6 : RingHomIsometric τ₁₂] {q : SeminormFamily 𝕝₂ F ι'} [inst_7 : TopologicalSpace E] [IsTopologicalAddGroup E] [inst_9 : TopologicalSpace F], WithSeminorms q → ∀ (f : E →ₛₗ[τ₁₂] F), Continuous ⇑f ↔ ∀ (i : ι'), Continuous ⇑((q i).comp f)
true
ContinuousMap.sigmaCodHomeomorph.match_1
Mathlib.Topology.ContinuousMap.Sigma
∀ (X : Type u_3) {ι : Type u_1} (Y : ι → Type u_2) [inst : TopologicalSpace X] [inst_1 : (i : ι) → TopologicalSpace (Y i)] (f : C(X, (i : ι) × Y i)) (motive : (∃ i g, f = (ContinuousMap.sigmaMk i).comp g) → Prop) (x : ∃ i g, f = (ContinuousMap.sigmaMk i).comp g), (∀ (i : ι) (g : C(X, Y i)) (hg : f = (ContinuousMap.sigmaMk i).comp g), motive ⋯) → motive x
false
Lean.Lsp.DocumentFilter.ctorIdx
Lean.Data.Lsp.Basic
Lean.Lsp.DocumentFilter → ℕ
false
_private.Init.Data.Dyadic.Basic.0.Dyadic.ble_iff_toRat._simp_1_1
Init.Data.Dyadic.Basic
∀ {x y : Dyadic}, (x.blt y = true) = (x.toRat < y.toRat)
false
NNRat.cast_zpow
Mathlib.Data.Rat.Cast.CharZero
∀ {α : Type u_3} [inst : DivisionSemiring α] [CharZero α] (q : ℚ≥0) (p : ℤ), ↑(q ^ p) = ↑q ^ p
true
OrderIso.subRight_symm_apply
Mathlib.Algebra.Order.Group.OrderIso
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [inst_2 : AddRightMono α] (a b : α), (RelIso.symm (OrderIso.subRight a)) b = b + a
true
Submodule.isHilbertSumOrthogonal
Mathlib.Analysis.InnerProductSpace.l2Space
∀ {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : CompleteSpace E] (K : Submodule 𝕜 E) [hK : CompleteSpace ↥K], IsHilbertSum 𝕜 (fun b => ↥(bif b then K else Kᗮ)) fun b => (bif b then K else Kᗮ).subtypeₗᵢ
true
List.min
Init.Data.List.Basic
{α : Type u} → [Min α] → (l : List α) → l ≠ [] → α
true
Filter.empty_notMem
Mathlib.Order.Filter.Basic
∀ {α : Type u} (f : Filter α) [f.NeBot], ∅ ∉ f
true
SeparationQuotient.instNormalSpace
Mathlib.Topology.Separation.Regular
∀ {X : Type u_1} [inst : TopologicalSpace X] [NormalSpace X], NormalSpace (SeparationQuotient X)
true
Lean.VersoModuleDocs.Snippet.addBlock
Lean.DocString.Extension
Lean.VersoModuleDocs.Snippet → Lean.Doc.Block Lean.ElabInline Lean.ElabBlock → Lean.VersoModuleDocs.Snippet
true
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.RotateLeft.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastRotateLeft._proof_5
Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.RotateLeft
∀ {w : ℕ} (distance curr : ℕ), curr < w → ¬curr + 1 ≤ w → False
false
Norm.mk
Mathlib.Analysis.Normed.Group.Defs
{E : Type u_8} → (E → ℝ) → Norm E
true
«term_∨_»
Init.Notation
Lean.TrailingParserDescr
true
ceilDiv_le_iff_le_mul
Mathlib.Algebra.Order.Floor.Div
∀ {α : Type u_2} [inst : Semiring α] [inst_1 : PartialOrder α] [inst_2 : CeilDiv α α] {a b c : α}, 0 < a → (b ⌈/⌉ a ≤ c ↔ b ≤ a * c)
true
BoundedOrderHom.dual_apply_toOrderHom
Mathlib.Order.Hom.Bounded
∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : BoundedOrder α] [inst_2 : Preorder β] [inst_3 : BoundedOrder β] (f : BoundedOrderHom α β), (BoundedOrderHom.dual f).toOrderHom = OrderHom.dual f.toOrderHom
true
DivisionRing.continuousConstSMul_rat
Mathlib.Topology.Algebra.Algebra.Rat
∀ {A : Type u_1} [inst : DivisionRing A] [inst_1 : TopologicalSpace A] [SeparatelyContinuousMul A] [inst_3 : CharZero A], ContinuousConstSMul ℚ A
true
RatFunc.denom_div_dvd
Mathlib.FieldTheory.RatFunc.Basic
∀ {K : Type u} [inst : Field K] (p q : Polynomial K), ((algebraMap (Polynomial K) (RatFunc K)) p / (algebraMap (Polynomial K) (RatFunc K)) q).denom ∣ q
true
Fin.map_rev_findRev?
Batteries.Data.Fin.Lemmas
∀ {n : ℕ} {p : Fin n → Bool}, Option.map Fin.rev (Fin.findRev? fun x => p x.rev) = Fin.find? p
true
CategoryTheory.CategoryOfElements.map._proof_2
Mathlib.CategoryTheory.Elements
∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {F₁ F₂ : CategoryTheory.Functor C (Type u_1)} (α : F₁ ⟶ F₂) (X : F₁.Elements), ⟨↑(CategoryTheory.CategoryStruct.id X), ⋯⟩ = CategoryTheory.CategoryStruct.id ⟨X.fst, α.app X.fst X.snd⟩
false
ProbabilityTheory.integrable_cauchyPDFReal
Mathlib.Probability.Distributions.Cauchy
∀ (x₀ : ℝ) {γ : NNReal}, MeasureTheory.Integrable (ProbabilityTheory.cauchyPDFReal x₀ γ) MeasureTheory.volume
true
_private.Mathlib.Data.Fin.Basic.0.Fin.coe_int_sub_eq_mod._proof_1_3
Mathlib.Data.Fin.Basic
∀ {n : ℕ} (u v : Fin n), ¬0 ≤ ↑↑u - ↑↑v + ↑n → False
false
dist_le_dist_of_le_pi
Mathlib.Analysis.Normed.Order.UpperLower
∀ {ι : Type u_2} [inst : Fintype ι] {a₁ a₂ b₁ b₂ : ι → ℝ}, a₂ ≤ a₁ → a₁ ≤ b₁ → b₁ ≤ b₂ → dist a₁ b₁ ≤ dist a₂ b₂
true
ClosedAddSubgroup.mk.sizeOf_spec
Mathlib.Topology.Algebra.Group.ClosedSubgroup
∀ {G : Type u} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [inst_2 : SizeOf G] (toAddSubgroup : AddSubgroup G) (isClosed' : IsClosed toAddSubgroup.carrier), sizeOf { toAddSubgroup := toAddSubgroup, isClosed' := isClosed' } = 1 + sizeOf toAddSubgroup + sizeOf isClosed'
true
_private.Mathlib.MeasureTheory.Measure.Hausdorff.0.MeasureTheory.Measure.hausdorffMeasure_zero_singleton._simp_1_2
Mathlib.MeasureTheory.Measure.Hausdorff
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] {p : α → Prop} [Nonempty α], (∀ᶠ (x : α) in Filter.atTop, p x) = ∃ a, ∀ b ≥ a, p b
false
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.LitValue.impureTypeScalarNumLit._sparseCasesOn_2
Lean.Compiler.LCNF.Basic
{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
FreeAddGroup.mk
Mathlib.GroupTheory.FreeGroup.Basic
{α : Type u} → List (α × Bool) → FreeAddGroup α
true
Nat.floor_natCast
Mathlib.Algebra.Order.Floor.Semiring
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [inst_2 : FloorSemiring R] [IsStrictOrderedRing R] (n : ℕ), ⌊↑n⌋₊ = n
true
CategoryTheory.LaxMonoidalFunctor.Hom.ctorIdx
Mathlib.CategoryTheory.Monoidal.NaturalTransformation
{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 G : CategoryTheory.LaxMonoidalFunctor C D} → F.Hom G → ℕ
false
_private.Init.Data.String.Decode.0.parseFirstByte_eq_done_of_utf8DecodeChar?_eq_some
Init.Data.String.Decode
∀ {b : ByteArray} {i : ℕ} {c : Char}, b.utf8DecodeChar? i = some c → c.utf8Size = 1 → ∀ (h' : i < b.size), ByteArray.utf8DecodeChar?.parseFirstByte b[i] = ByteArray.utf8DecodeChar?.FirstByte.done
true
Aesop.SearchM.instMonad
Aesop.Search.SearchM
{Q : Type} → [inst : Aesop.Queue Q] → Monad (Aesop.SearchM Q)
true
NNReal.rpow_sub_one'
Mathlib.Analysis.SpecialFunctions.Pow.NNReal
∀ {y : ℝ}, y - 1 ≠ 0 → ∀ (x : NNReal), x ^ (y - 1) = x ^ y / x
true
cyclotomicCharacter.toFun._proof_1
Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter
∀ (p : ℕ) [Fact (Nat.Prime p)] (x : ℕ), NeZero (p ^ x)
false
Quiver.Path.vertices_ne_nil
Mathlib.Combinatorics.Quiver.Path.Vertices
∀ {V : Type u_1} [inst : Quiver V] {a b : V} (p : Quiver.Path a b), p.vertices ≠ []
true
Pi.constMonoidHom._proof_2
Mathlib.Algebra.Group.Pi.Lemmas
∀ (α : Type u_1) (β : Type u_2) [inst : MulOneClass β] (x x_1 : β), Function.const α (x * x_1) = Function.const α (x * x_1)
false
CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.ofIso._proof_3
Mathlib.AlgebraicTopology.ExtraDegeneracy
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : CategoryTheory.SimplicialObject.Augmented C} (e : X ≅ Y) (ed : X.ExtraDegeneracy), CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp ((CategoryTheory.SimplicialObject.Augmented.drop.mapIso e).inv.app (Opposite.op (SimplexCategory.mk 0))) (CategoryTheory.CategoryStruct.comp (ed.s 0) ((CategoryTheory.SimplicialObject.Augmented.drop.mapIso e).hom.app (Opposite.op (SimplexCategory.mk (0 + 1)))))) (Y.left.δ 1) = CategoryTheory.CategoryStruct.comp (Y.hom.app (Opposite.op (SimplexCategory.mk 0))) (CategoryTheory.CategoryStruct.comp (CategoryTheory.SimplicialObject.Augmented.point.mapIso e).inv (CategoryTheory.CategoryStruct.comp ed.s' ((CategoryTheory.SimplicialObject.Augmented.drop.mapIso e).hom.app (Opposite.op (SimplexCategory.mk 0)))))
false
IsDedekindFiniteAddMonoid.rec
Mathlib.Algebra.Group.Defs
{M : Type u_2} → [inst : AddZero M] → {motive : IsDedekindFiniteAddMonoid M → Sort u} → ((add_eq_zero_symm : ∀ {a b : M}, a + b = 0 → b + a = 0) → motive ⋯) → (t : IsDedekindFiniteAddMonoid M) → motive t
false
Lean.Meta.MVarRenaming.mk.injEq
Lean.Meta.Match.MVarRenaming
∀ (map map_1 : Lean.MVarIdMap Lean.MVarId), ({ map := map } = { map := map_1 }) = (map = map_1)
true
Lean.Elab.WF.GuessLex.RecCallWithContext.rec
Lean.Elab.PreDefinition.WF.GuessLex
{motive : Lean.Elab.WF.GuessLex.RecCallWithContext → Sort u} → ((ref : Lean.Syntax) → (caller : ℕ) → (params : Array Lean.Expr) → (callee : ℕ) → (args : Array Lean.Expr) → (ctxt : Lean.Elab.WF.GuessLex.SavedLocalContext) → motive { ref := ref, caller := caller, params := params, callee := callee, args := args, ctxt := ctxt }) → (t : Lean.Elab.WF.GuessLex.RecCallWithContext) → motive t
false
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.assemble₄_eq_some_of_toBitVec._simp_1_6
Init.Data.String.Decode
∀ {n : ℕ} {x y : BitVec n}, (x ≤ y) = (x.toNat ≤ y.toNat)
false
TopCat.uliftFunctor._proof_2
Mathlib.Topology.Category.TopCat.ULift
∀ (X : TopCat), TopCat.ofHom { toFun := ULift.map ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.id X)), continuous_toFun := ⋯ } = CategoryTheory.CategoryStruct.id (TopCat.of (ULift.{u_2, u_1} ↑X))
false
FormalMultilinearSeries.iteratedFDerivSeries._proof_5
Mathlib.Analysis.Analytic.IteratedFDeriv
∀ {𝕜 : Type u_3} [inst : NontriviallyNormedField 𝕜] {E : Type u_1} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {F : Type u_2} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (k : ℕ), ContinuousAdd (ContinuousMultilinearMap 𝕜 (fun i => E) F)
false
Complex.real_le_real
Mathlib.Analysis.Complex.Order
∀ {x y : ℝ}, ↑x ≤ ↑y ↔ x ≤ y
true
NumberField.ComplexEmbedding.IsConj.ext_iff
Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings
∀ {K : Type u_1} [inst : Field K] {k : Type u_2} [inst_1 : Field k] [inst_2 : Algebra k K] {φ : K →+* ℂ} {σ₁ σ₂ : Gal(K/k)}, NumberField.ComplexEmbedding.IsConj φ σ₁ → (σ₁ = σ₂ ↔ NumberField.ComplexEmbedding.IsConj φ σ₂)
true
CategoryTheory.StrictlyUnitaryPseudofunctor.casesOn
Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary
{B : Type u₁} → [inst : CategoryTheory.Bicategory B] → {C : Type u₂} → [inst_1 : CategoryTheory.Bicategory C] → {motive : CategoryTheory.StrictlyUnitaryPseudofunctor B C → Sort u} → (t : CategoryTheory.StrictlyUnitaryPseudofunctor B C) → ((toPseudofunctor : CategoryTheory.Pseudofunctor B C) → (map_id : ∀ (X : B), toPseudofunctor.map (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id (toPseudofunctor.obj X)) → (mapId_eq_eqToIso : ∀ (X : B), toPseudofunctor.mapId X = CategoryTheory.eqToIso ⋯) → motive { toPseudofunctor := toPseudofunctor, map_id := map_id, mapId_eq_eqToIso := mapId_eq_eqToIso }) → motive t
false
Std.DHashMap.Internal.Raw₀.Const.insertMany_list_equiv_congr
Std.Data.DHashMap.Internal.RawLemmas
∀ {α : Type u} [inst : BEq α] [inst_1 : Hashable α] {β : Type v} (m₁ m₂ : Std.DHashMap.Internal.Raw₀ α fun x => β) [EquivBEq α] [LawfulHashable α], (↑m₁).WF → (↑m₂).WF → (↑m₁).Equiv ↑m₂ → ∀ {l : List (α × β)}, (↑↑(Std.DHashMap.Internal.Raw₀.Const.insertMany m₁ l)).Equiv ↑↑(Std.DHashMap.Internal.Raw₀.Const.insertMany m₂ l)
true
SetLike.gsemiring._proof_7
Mathlib.Algebra.DirectSum.Internal
∀ {ι : Type u_3} {σ : Type u_2} {R : Type u_1} [inst : AddMonoid ι] [inst_1 : Semiring R] [inst_2 : SetLike σ R] [AddSubmonoidClass σ R] (A : ι → σ) [SetLike.GradedMonoid A] (n : ℕ), ↑n ∈ A 0
false
_private.Lean.Data.PersistentHashMap.0.Lean.PersistentHashMap.insertAux.match_1
Lean.Data.PersistentHashMap
{α : Type u_1} → {β : Type u_2} → (motive : Lean.PersistentHashMap.CollisionNode α β → Sort u_3) → (newNode : Lean.PersistentHashMap.CollisionNode α β) → ((es : Array (Lean.PersistentHashMap.Entry α β (Lean.PersistentHashMap.Node α β))) → (h : Lean.PersistentHashMap.IsCollisionNode (Lean.PersistentHashMap.Node.entries es)) → motive ⟨Lean.PersistentHashMap.Node.entries es, h⟩) → ((keys : Array α) → (vals : Array β) → (heq : keys.size = vals.size) → (property : Lean.PersistentHashMap.IsCollisionNode (Lean.PersistentHashMap.Node.collision keys vals heq)) → motive ⟨Lean.PersistentHashMap.Node.collision keys vals heq, property⟩) → motive newNode
false
Height.logHeight₁_div_eq_logHeight
Mathlib.NumberTheory.Height.Basic
∀ {K : Type u_1} [inst : Field K] [inst_1 : Height.AdmissibleAbsValues K] (x y : K), Height.logHeight₁ (x / y) = Height.logHeight ![x, y]
true
Mathlib.Meta.NormNum.IsNat.nnreal_rpow_eq_nnreal_pow
Mathlib.Analysis.SpecialFunctions.Pow.NNReal
∀ {b : ℝ} {n : ℕ}, Mathlib.Meta.NormNum.IsNat b n → ∀ (a : NNReal), a ^ b = a ^ n
true
Lean.LOption.casesOn
Lean.Data.LOption
{α : Type u} → {motive : Lean.LOption α → Sort u_1} → (t : Lean.LOption α) → motive Lean.LOption.none → ((a : α) → motive (Lean.LOption.some a)) → motive Lean.LOption.undef → motive t
false
_private.Mathlib.CategoryTheory.Sites.IsSheafFor.0.CategoryTheory.Presieve.isSheafFor_bind._proof_1_11
Mathlib.CategoryTheory.Sites.IsSheafFor
∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {X : C} (P : CategoryTheory.Functor Cᵒᵖ (Type u_1)) (U : CategoryTheory.Sieve X) (B : ⦃Y : C⦄ → ⦃f : Y ⟶ X⦄ → U.arrows f → CategoryTheory.Sieve Y) (hB : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄ (hf : U.arrows f), CategoryTheory.Presieve.IsSheafFor P (B hf).arrows) (s : CategoryTheory.Presieve.FamilyOfElements P (CategoryTheory.Sieve.bind U.arrows B).arrows) (hy : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄ (hf : U.arrows f), CategoryTheory.Presieve.FamilyOfElements.Compatible ((fun Y f hf Z g hg => s (CategoryTheory.CategoryStruct.comp g f) ⋯) Y f hf)) ⦃Z W : C⦄ (f : Z ⟶ X) (h : W ⟶ Z) (hf : U.arrows f) ⦃Y : C⦄ ⦃l : Y ⟶ W⦄ (hl : (B ⋯).arrows l) ⦃M : C⦄ ⦃m : M ⟶ Y⦄ (this : (CategoryTheory.Sieve.bind U.arrows B).arrows (CategoryTheory.CategoryStruct.comp m (CategoryTheory.CategoryStruct.comp l (CategoryTheory.CategoryStruct.comp h f)))), P.map m.op (P.map l.op ((fun Y f hf => ⋯.amalgamate ((fun Y f hf Z g hg => s (CategoryTheory.CategoryStruct.comp g f) ⋯) Y f hf) ⋯) W (CategoryTheory.CategoryStruct.comp h f) ⋯)) = (fun Y f hf Z g hg => s (CategoryTheory.CategoryStruct.comp g f) ⋯) W (CategoryTheory.CategoryStruct.comp h f) ⋯ M (CategoryTheory.CategoryStruct.comp m l) ⋯ → P.map m.op (P.map l.op ((fun Y f hf => ⋯.amalgamate ((fun Y f hf Z g hg => s (CategoryTheory.CategoryStruct.comp g f) ⋯) Y f hf) ⋯) W (CategoryTheory.CategoryStruct.comp h f) ⋯)) = s (CategoryTheory.CategoryStruct.comp m (CategoryTheory.CategoryStruct.comp l (CategoryTheory.CategoryStruct.comp h f))) this
false
SuccAddOrder.noConfusionType
Mathlib.Algebra.Order.SuccPred
Sort u → {α : Type u_1} → [inst : Preorder α] → [inst_1 : Add α] → [inst_2 : One α] → SuccAddOrder α → {α' : Type u_1} → [inst' : Preorder α'] → [inst'_1 : Add α'] → [inst'_2 : One α'] → SuccAddOrder α' → Sort u
false
CategoryTheory.Mon.trivial_mon_mul
Mathlib.CategoryTheory.Monoidal.Mon_
∀ (C : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C], CategoryTheory.MonObj.mul = (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).hom
true
_private.Mathlib.Tactic.DefEqAbuse.0.Lean.MessageData.visitTraceNodesM.go.match_1
Mathlib.Tactic.DefEqAbuse
{α : Type} → (motive : Lean.MessageData.VisitStep✝ α → Sort u_1) → (__do_lift : Lean.MessageData.VisitStep✝¹ α) → ((a? : Option α) → motive (Lean.MessageData.VisitStep.descend✝ a?)) → ((a? : Option α) → motive (Lean.MessageData.VisitStep.ascend✝ a?)) → motive __do_lift
false
_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_singleton_left._simp_1_3
Mathlib.Data.Finset.Disjoint
∀ {α : Sort u_1} {p : α → Prop} {a' : α}, (∀ (a : α), a = a' → p a) = p a'
false
Metric.Snowflaking.uniformContinuous_toSnowflaking
Mathlib.Topology.MetricSpace.Snowflaking
∀ {X : Type u_1} {α : ℝ} {hα₀ : 0 < α} {hα₁ : α ≤ 1} [inst : UniformSpace X], UniformContinuous ⇑Metric.Snowflaking.toSnowflaking
true
continouousOn_union_iff_of_isClosed
Mathlib.Topology.ContinuousOn
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s t : Set α} {f : α → β}, IsClosed s → IsClosed t → (ContinuousOn f (s ∪ t) ↔ ContinuousOn f s ∧ ContinuousOn f t)
true
Algebra.FiniteType.mk._flat_ctor
Mathlib.RingTheory.FiniteType
∀ {R : Type uR} {A : Type uA} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A], ⊤.FG → Algebra.FiniteType R A
false
_private.Mathlib.Tactic.CategoryTheory.Bicategory.PureCoherence.0.Mathlib.Tactic.Bicategory._aux_Mathlib_Tactic_CategoryTheory_Bicategory_PureCoherence___unexpand_CategoryTheory_Bicategory_whiskerLeftIso_1
Mathlib.Tactic.CategoryTheory.Bicategory.PureCoherence
Lean.PrettyPrinter.Unexpander
false
AddSubgroup.isOpen_of_mem_nhds
Mathlib.Topology.Algebra.OpenSubgroup
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousAdd G] (H : AddSubgroup G) {g : G}, ↑H ∈ nhds g → IsOpen ↑H
true
fderivWithin_comp_derivWithin
Mathlib.Analysis.Calculus.Deriv.Comp
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace 𝕜 F] {E : Type w} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f : 𝕜 → F} (x : 𝕜) {s : Set 𝕜} {l : F → E} {t : Set F}, DifferentiableWithinAt 𝕜 l t (f x) → DifferentiableWithinAt 𝕜 f s x → Set.MapsTo f s t → derivWithin (l ∘ f) s x = (fderivWithin 𝕜 l t (f x)) (derivWithin f s x)
true
LinearMap.BilinForm.ker_restrict_eq_of_codisjoint
Mathlib.LinearAlgebra.BilinearForm.Orthogonal
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {p q : Submodule R M}, Codisjoint p q → ∀ {B : LinearMap.BilinForm R M}, (∀ x ∈ p, ∀ y ∈ q, (B x) y = 0) → LinearMap.ker (B.restrict p) = Submodule.comap p.subtype (LinearMap.ker B)
true
Std.HashMap.Raw.size_alter_le_size
Std.Data.HashMap.RawLemmas
∀ {α : Type u} {β : Type v} [inst : BEq α] [inst_1 : Hashable α] {m : Std.HashMap.Raw α β} [inst_2 : LawfulBEq α] {k : α} {f : Option β → Option β}, m.WF → (m.alter k f).size ≤ m.size + 1
true
contDiff_norm_sq
Mathlib.Analysis.InnerProductSpace.Calculus
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [inst : NormedSpace ℝ E] {n : WithTop ℕ∞}, ContDiff ℝ n fun x => ‖x‖ ^ 2
true
CategoryTheory.Functor.partialRightAdjoint._proof_2
Mathlib.CategoryTheory.Adjunction.PartialAdjoint
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {D : Type u_4} [inst_1 : CategoryTheory.Category.{u_3, u_4} D] (F : CategoryTheory.Functor C D) {X Y Z : F.PartialRightAdjointSource} (f : X ⟶ Y) (g : Y ⟶ Z), F.partialRightAdjointMap (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (F.partialRightAdjointMap f) (F.partialRightAdjointMap g)
false
PiTensorProduct.dualDistribInvOfBasis._proof_3
Mathlib.LinearAlgebra.PiTensorProduct.Dual
∀ {ι : Type u_2} {R : Type u_1} {M : ι → Type u_3} [inst : CommRing R] [inst_1 : (i : ι) → AddCommGroup (M i)] [inst_2 : (i : ι) → Module R (M i)], SMulCommClass R ℕ (PiTensorProduct R fun i => Module.Dual R (M i))
false
CategoryTheory.Mat.equivalenceSingleObjInverse._proof_1
Mathlib.CategoryTheory.Preadditive.Mat
∀ (R : Type) [inst : Ring R] (X : CategoryTheory.Mat_ (CategoryTheory.SingleObj Rᵐᵒᵖ)), (fun i j => MulOpposite.unop (CategoryTheory.CategoryStruct.id X i j)) = CategoryTheory.CategoryStruct.id (FintypeCat.of X.ι)
false
Std.DTreeMap.Internal.RocSlice
Std.Data.DTreeMap.Internal.Zipper
(α : Type u_1) → (α → Type u_2) → [Ord α] → Type (max u_2 u_1)
true
_private.Lean.Meta.Tactic.TryThis.0.Lean.Meta.Tactic.TryThis.tryThisProvider
Lean.Meta.Tactic.TryThis
Lean.Server.CodeActionProvider
true
Lean.Linter.UnusedVariables.References.recOn
Lean.Linter.UnusedVariables
{motive : Lean.Linter.UnusedVariables.References → Sort u} → (t : Lean.Linter.UnusedVariables.References) → ((constDecls : Std.HashSet Lean.Syntax.Range) → (fvarDefs : Std.HashMap Lean.Syntax.Range Lean.Linter.UnusedVariables.FVarDefinition) → (fvarUses : Std.HashSet Lean.FVarId) → (fvarAliases : Std.HashMap Lean.FVarId Lean.FVarId) → (assignments : Array (Lean.PersistentHashMap Lean.MVarId Lean.Expr)) → motive { constDecls := constDecls, fvarDefs := fvarDefs, fvarUses := fvarUses, fvarAliases := fvarAliases, assignments := assignments }) → motive t
false
_private.Lean.PrettyPrinter.Delaborator.Builtins.0.Lean.PrettyPrinter.Delaborator.collectStructFields._unsafe_rec
Lean.PrettyPrinter.Delaborator.Builtins
Lean.Name → List Lean.Level → Array Lean.Expr → Array (Lean.TSyntax `Lean.Parser.Term.structInstField) → Lean.NameMap Lean.Expr → Lean.ConstructorVal → Lean.PrettyPrinter.Delaborator.DelabM (Lean.NameMap Lean.Expr × Array (Lean.TSyntax `Lean.Parser.Term.structInstField))
false