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5.42M
cfc_mono._auto_1
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital
Lean.Syntax
Set.MapsTo.inter_inter
Mathlib.Data.Set.Function
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t₁ t₂ : Set β} {f : α → β}, Set.MapsTo f s₁ t₁ → Set.MapsTo f s₂ t₂ → Set.MapsTo f (s₁ ∩ s₂) (t₁ ∩ t₂)
Fin.succ_eq_last_succ
Init.Data.Fin.Lemmas
∀ {n : ℕ} {i : Fin n.succ}, i.succ = Fin.last (n + 1) ↔ i = Fin.last n
R0Space.specializes_symmetric
Mathlib.Topology.Separation.Basic
∀ {X : Type u} {inst : TopologicalSpace X} [self : R0Space X], Symmetric Specializes
UpperHalfPlane.verticalStrip
Mathlib.Analysis.Complex.UpperHalfPlane.Topology
ℝ → ℝ → Set UpperHalfPlane
BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_BoundedCompactlySupported___unexpand_compactlySupported_1
Mathlib.Topology.ContinuousMap.BoundedCompactlySupported
Lean.PrettyPrinter.Unexpander
CategoryTheory.Limits.parallelPairHom._proof_4
Mathlib.CategoryTheory.Limits.Shapes.Equalizers
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y X' Y' : C} (f g : X ⟶ Y) (f' g' : X' ⟶ Y') (p : X ⟶ X') (q : Y ⟶ Y'), CategoryTheory.CategoryStruct.comp g q = CategoryTheory.CategoryStruct.comp p g' → CategoryTheory.CategoryStruct.comp ((CategoryTheory.Limits.parallelPair f g).map CategoryTheory.Limits.WalkingParallelPairHom.right) q = CategoryTheory.CategoryStruct.comp p ((CategoryTheory.Limits.parallelPair f' g').map CategoryTheory.Limits.WalkingParallelPairHom.right)
GenContFract.convs'Aux_stable_step_of_terminated
Mathlib.Algebra.ContinuedFractions.TerminatedStable
∀ {K : Type u_1} {n : ℕ} [inst : DivisionRing K] {s : Stream'.Seq (GenContFract.Pair K)}, s.TerminatedAt n → GenContFract.convs'Aux s (n + 1) = GenContFract.convs'Aux s n
Turing.TM0.Stmt.move.inj
Mathlib.Computability.PostTuringMachine
∀ {Γ : Type u_1} {a a_1 : Turing.Dir}, Turing.TM0.Stmt.move a = Turing.TM0.Stmt.move a_1 → a = a_1
CliffordAlgebra.GradedAlgebra.ι
Mathlib.LinearAlgebra.CliffordAlgebra.Grading
{R : Type u_1} → {M : Type u_2} → [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (Q : QuadraticForm R M) → M →ₗ[R] DirectSum (ZMod 2) fun i => ↥(CliffordAlgebra.evenOdd Q i)
Cardinal.isInaccessible_def
Mathlib.SetTheory.Cardinal.Regular
∀ {c : Cardinal.{u_1}}, c.IsInaccessible ↔ Cardinal.aleph0 < c ∧ c.IsRegular ∧ c.IsStrongLimit
Char.ltAsymm
Init.Data.Char.Lemmas
Std.Asymm fun x1 x2 => x1 < x2
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.foldlM.eq_def
Std.Data.DHashMap.Internal.AssocList.Lemmas
∀ {α : Type u} {β : α → Type v} {δ : Type w} {m : Type w → Type w'} [inst : Monad m] (f : δ → (a : α) → β a → m δ) (x : δ) (x_1 : Std.DHashMap.Internal.AssocList α β), Std.DHashMap.Internal.AssocList.foldlM f x x_1 = match x, x_1 with | d, Std.DHashMap.Internal.AssocList.nil => pure d | d, Std.DHashMap.Internal.AssocList.cons a b es => do let d ← f d a b Std.DHashMap.Internal.AssocList.foldlM f d es
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.evalAlts.goWithIncremental._proof_1
Lean.Elab.Tactic.Induction
∀ (r : Array Lean.Elab.Tactic.ElimApp.Alt) (i : Fin r.size), ↑i < r.size
List.min?_cons'
Init.Data.List.MinMax
∀ {α : Type u_1} {x : α} [inst : Min α] {xs : List α}, (x :: xs).min? = some (List.foldl min x xs)
UniformSpace.Completion.instNormedSpace._proof_2
Mathlib.Analysis.Normed.Module.Completion
∀ (𝕜 : Type u_1) (E : Type u_2) [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E], UniformContinuousConstSMul 𝕜 E
CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone._proof_2
Mathlib.CategoryTheory.Limits.Constructions.Filtered
∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} C] {α : Type u_1} [inst_1 : CategoryTheory.Limits.HasFiniteCoproducts C] [CategoryTheory.Limits.HasColimitsOfShape (Finset (CategoryTheory.Discrete α)) C] (F : CategoryTheory.Functor (CategoryTheory.Discrete α) C), CategoryTheory.Limits.HasColimit (CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj F)
Std.Tactic.BVDecide.LRAT.Internal.Clause.mk.noConfusion
Std.Tactic.BVDecide.LRAT.Internal.Clause
{α : outParam (Type u)} → {β : Type v} → {P : Sort u_1} → {toList : β → Std.Sat.CNF.Clause α} → {not_tautology : ∀ (c : β) (l : Std.Sat.Literal α), l ∉ toList c ∨ l.negate ∉ toList c} → {ofArray : Array (Std.Sat.Literal α) → Option β} → {empty : β} → {empty_eq : toList empty = []} → {unit : Std.Sat.Literal α → β} → {unit_eq : ∀ (l : Std.Sat.Literal α), toList (unit l) = [l]} → {isUnit : β → Option (Std.Sat.Literal α)} → {isUnit_iff : ∀ (c : β) (l : Std.Sat.Literal α), isUnit c = some l ↔ toList c = [l]} → {negate : β → Std.Sat.CNF.Clause α} → {negate_eq : ∀ (c : β), negate c = List.map Std.Sat.Literal.negate (toList c)} → {delete : β → Std.Sat.Literal α → β} → {delete_iff : ∀ (c : β) (l l' : Std.Sat.Literal α), l' ∈ toList (delete c l) ↔ l' ≠ l ∧ l' ∈ toList c} → {contains : β → Std.Sat.Literal α → Bool} → {contains_iff : ∀ (c : β) (l : Std.Sat.Literal α), contains c l = true ↔ l ∈ toList c} → {reduce : β → Array Std.Tactic.BVDecide.LRAT.Internal.Assignment → Std.Tactic.BVDecide.LRAT.Internal.ReduceResult α} → {toList' : β → Std.Sat.CNF.Clause α} → {not_tautology' : ∀ (c : β) (l : Std.Sat.Literal α), l ∉ toList' c ∨ l.negate ∉ toList' c} → {ofArray' : Array (Std.Sat.Literal α) → Option β} → {empty' : β} → {empty_eq' : toList' empty' = []} → {unit' : Std.Sat.Literal α → β} → {unit_eq' : ∀ (l : Std.Sat.Literal α), toList' (unit' l) = [l]} → {isUnit' : β → Option (Std.Sat.Literal α)} → {isUnit_iff' : ∀ (c : β) (l : Std.Sat.Literal α), isUnit' c = some l ↔ toList' c = [l]} → {negate' : β → Std.Sat.CNF.Clause α} → {negate_eq' : ∀ (c : β), negate' c = List.map Std.Sat.Literal.negate (toList' c)} → {delete' : β → Std.Sat.Literal α → β} → {delete_iff' : ∀ (c : β) (l l' : Std.Sat.Literal α), l' ∈ toList' (delete' c l) ↔ l' ≠ l ∧ l' ∈ toList' c} → {contains' : β → Std.Sat.Literal α → Bool} → {contains_iff' : ∀ (c : β) (l : Std.Sat.Literal α), contains' c l = true ↔ l ∈ toList' c} → {reduce' : β → Array Std.Tactic.BVDecide.LRAT.Internal.Assignment → Std.Tactic.BVDecide.LRAT.Internal.ReduceResult α} → { toList := toList, not_tautology := not_tautology, ofArray := ofArray, empty := empty, empty_eq := empty_eq, unit := unit, unit_eq := unit_eq, isUnit := isUnit, isUnit_iff := isUnit_iff, negate := negate, negate_eq := negate_eq, delete := delete, delete_iff := delete_iff, contains := contains, contains_iff := contains_iff, reduce := reduce } = { toList := toList', not_tautology := not_tautology', ofArray := ofArray', empty := empty', empty_eq := empty_eq', unit := unit', unit_eq := unit_eq', isUnit := isUnit', isUnit_iff := isUnit_iff', negate := negate', negate_eq := negate_eq', delete := delete', delete_iff := delete_iff', contains := contains', contains_iff := contains_iff', reduce := reduce' } → (toList ≍ toList' → ofArray ≍ ofArray' → empty ≍ empty' → unit ≍ unit' → isUnit ≍ isUnit' → negate ≍ negate' → delete ≍ delete' → contains ≍ contains' → reduce ≍ reduce' → P) → P
Stream'.WSeq.productive_dropn
Mathlib.Data.WSeq.Productive
∀ {α : Type u} (s : Stream'.WSeq α) [s.Productive] (n : ℕ), (s.drop n).Productive
Submodule.Quotient.instSMul'
Mathlib.LinearAlgebra.Quotient.Defs
{R : Type u_1} → {M : Type u_2} → [inst : Ring R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → {S : Type u_3} → [inst_3 : SMul S R] → [inst_4 : SMul S M] → [IsScalarTower S R M] → (P : Submodule R M) → SMul S (M ⧸ P)
Std.ExtDHashMap.mem_alter
Std.Data.ExtDHashMap.Lemmas
∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {β : α → Type v} {m : Std.ExtDHashMap α β} [inst : LawfulBEq α] {k k' : α} {f : Option (β k) → Option (β k)}, k' ∈ m.alter k f ↔ if (k == k') = true then (f (m.get? k)).isSome = true else k' ∈ m
IsCompact.exists_thickening_image_subset
Mathlib.Topology.MetricSpace.Thickening
∀ {α : Type u} [inst : PseudoEMetricSpace α] {β : Type u_2} [inst_1 : PseudoEMetricSpace β] {f : α → β} {K : Set α} {U : Set β}, IsCompact K → IsOpen U → (∀ x ∈ K, ContinuousAt f x) → Set.MapsTo f K U → ∃ ε > 0, ∃ V ∈ nhdsSet K, Metric.thickening ε (f '' V) ⊆ U
Lean.Lsp.instHashableRpcRef
Lean.Server.Rpc.Basic
Hashable Lean.Lsp.RpcRef
CategoryTheory.sum.inrCompInverseAssociator_inv_app
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 : D ⊕ E), (CategoryTheory.sum.inrCompInverseAssociator C D E).inv.app X = CategoryTheory.CategoryStruct.id ((((CategoryTheory.Sum.inr_ C D).comp (CategoryTheory.Sum.inl_ (C ⊕ D) E)).sum' (CategoryTheory.Sum.inr_ (C ⊕ D) E)).obj X)
Std.DTreeMap.Internal.Const.RoiSliceData.rec
Std.Data.DTreeMap.Internal.Zipper
{α : Type u} → {β : Type v} → [inst : Ord α] → {motive : Std.DTreeMap.Internal.Const.RoiSliceData α β → Sort u_1} → ((treeMap : Std.DTreeMap.Internal.Impl α fun x => β) → (range : Std.Roi α) → motive { treeMap := treeMap, range := range }) → (t : Std.DTreeMap.Internal.Const.RoiSliceData α β) → motive t
MvPolynomial.supported.eq_1
Mathlib.Algebra.MvPolynomial.Supported
∀ {σ : Type u_1} (R : Type u) [inst : CommSemiring R] (s : Set σ), MvPolynomial.supported R s = Algebra.adjoin R (MvPolynomial.X '' s)
MeasureTheory.SimpleFunc.instLattice._proof_1
Mathlib.MeasureTheory.Function.SimpleFunc
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : Lattice β] (a b : MeasureTheory.SimpleFunc α β), SemilatticeInf.inf a b ≤ a
Subsemigroup.le_comap_map
Mathlib.Algebra.Group.Subsemigroup.Operations
∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] (S : Subsemigroup M) {f : M →ₙ* N}, S ≤ Subsemigroup.comap f (Subsemigroup.map f S)
ProbabilityTheory.Kernel.comap._proof_1
Mathlib.Probability.Kernel.Composition.MapComap
∀ {α : Type u_3} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_1} {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) (g : γ → α), Measurable g → Measurable (⇑κ ∘ g)
MonoidHom.toLocalizationMap._proof_2
Mathlib.GroupTheory.MonoidLocalization.Basic
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N] (f : M →* N), (∀ (y : ↥S), IsUnit (f ↑y)) → (∀ (z : N), ∃ x, z * f ↑x.2 = f x.1) → (∀ (x y : M), f x = f y → ∃ c, ↑c * x = ↑c * y) → S.IsLocalizationMap (↑f).toFun
Real.not_DifferentiableAt_log_mul_zero
Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
¬DifferentiableAt ℝ (fun x => x * Real.log x) 0
Mathlib.Tactic.CancelDenoms.CancelResult.recOn
Mathlib.Tactic.CancelDenoms.Core
{u : Lean.Level} → {α : Q(Type u)} → {mα : Q(Mul «$α»)} → {e v : Q(«$α»)} → {motive : Mathlib.Tactic.CancelDenoms.CancelResult mα e v → Sort u} → (t : Mathlib.Tactic.CancelDenoms.CancelResult mα e v) → ((cancelled : Q(«$α»)) → (pf : Q(«$v» * «$e» = «$cancelled»)) → motive { cancelled := cancelled, pf := pf }) → motive t
_private.Lean.Elab.Do.Legacy.0.Lean.Elab.Term.Do.destructTuple._proof_2
Lean.Elab.Do.Legacy
∀ (uvars : Array Lean.Elab.Term.Do.Var), uvars.size = 1 → 0 < uvars.size
NormedAddGroupHom.range_comp_incl_top
Mathlib.Analysis.Normed.Group.Hom
∀ {V₁ : Type u_3} {V₂ : Type u_4} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂] (f : NormedAddGroupHom V₁ V₂), (f.comp (NormedAddGroupHom.incl ⊤)).range = f.range
_private.Init.Data.Slice.Array.Lemmas.0.Std.Internal.List.extract_eq_drop_take'._simp_1_5
Init.Data.Slice.Array.Lemmas
∀ {α : Type u_1} [inst : LE α] {x y : α}, (x ≥ y) = (y ≤ x)
Std.TreeMap.Raw.getKey!_union
Std.Data.TreeMap.Raw.Lemmas
∀ {α : Type u} {β : Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.TreeMap.Raw α β cmp} [Std.TransCmp cmp] [inst : Inhabited α], t₁.WF → t₂.WF → ∀ {k : α}, (t₁ ∪ t₂).getKey! k = t₂.getKeyD k (t₁.getKey! k)
MvPFunctor.instMvQPFObj
Mathlib.Data.QPF.Multivariate.Basic
{n : ℕ} → (P : MvPFunctor.{u_1} n) → MvQPF ↑P
mem_upperBounds_image2_of_mem_lowerBounds
Mathlib.Order.Bounds.Image
∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ] {f : α → β → γ} {s : Set α} {t : Set β} {a : α} {b : β}, (∀ (b : β), Antitone (Function.swap f b)) → (∀ (a : α), Antitone (f a)) → a ∈ lowerBounds s → b ∈ lowerBounds t → f a b ∈ upperBounds (Set.image2 f s t)
Nat.Partrec.Code.evaln._unary._proof_7
Mathlib.Computability.PartrecCode
∀ (k : ℕ) (cf cg : Nat.Partrec.Code), (invImage (fun x => PSigma.casesOn x fun a a_1 => (a, a_1)) Prod.instWellFoundedRelation).1 ⟨k, cf.prec cg⟩ ⟨k.succ, cf.prec cg⟩
SMulPosStrictMono.toSMulPosMono
Mathlib.Algebra.Order.Module.Defs
∀ {α : Type u_1} {β : Type u_2} [inst : Zero α] [inst_1 : Zero β] [inst_2 : SMulWithZero α β] [inst_3 : PartialOrder α] [inst_4 : PartialOrder β] [SMulPosStrictMono α β], SMulPosMono α β
DependsOn.dependsOn_lmarginalPartialTraj
Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj
∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)} {b : ℕ} {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))} [∀ (n : ℕ), ProbabilityTheory.IsSFiniteKernel (κ n)] (a : ℕ) {f : ((n : ℕ) → X n) → ENNReal}, DependsOn f ↑(Finset.Iic b) → Measurable f → DependsOn (ProbabilityTheory.Kernel.lmarginalPartialTraj κ a b f) ↑(Finset.Iic a)
CategoryTheory.Limits.Concrete.limit_ext
Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type r} [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {J : Type w} [inst_3 : CategoryTheory.Category.{t, w} J] (F : CategoryTheory.Functor J C) [CategoryTheory.Limits.PreservesLimit F (CategoryTheory.forget C)] [inst_5 : CategoryTheory.Limits.HasLimit F] (x y : CategoryTheory.ToType (CategoryTheory.Limits.limit F)), (∀ (j : J), (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j)) x = (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j)) y) → x = y
Std.ExtDTreeMap.getKey!_inter_of_not_mem_right
Std.Data.ExtDTreeMap.Lemmas
∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.ExtDTreeMap α β cmp} [inst : Inhabited α] [inst_1 : Std.TransCmp cmp] {k : α}, k ∉ t₂ → (t₁ ∩ t₂).getKey! k = default
List.find?_replicate_eq_some_iff._simp_1
Init.Data.List.Find
∀ {α : Type u_1} {n : ℕ} {a b : α} {p : α → Bool}, (List.find? p (List.replicate n a) = some b) = (n ≠ 0 ∧ p a = true ∧ a = b)
Lean.IR.Expr.ctor
Lean.Compiler.IR.Basic
Lean.IR.CtorInfo → Array Lean.IR.Arg → Lean.IR.Expr
OpenNormalSubgroup.pathComponentOne.eq_1
Mathlib.Topology.Connected.PathComponentOne
∀ (G : Type u_1) [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G] [inst_3 : LocPathConnectedSpace G], OpenNormalSubgroup.pathComponentOne G = { toSubgroup := Subgroup.pathComponentOne G, isOpen' := ⋯, isNormal' := ⋯ }
Lean.Meta.MVarRenaming.map._default
Lean.Meta.Match.MVarRenaming
Lean.MVarIdMap Lean.MVarId
UInt16.neg_ne_zero
Init.Data.UInt.Lemmas
∀ {a : UInt16}, -a ≠ 0 ↔ a ≠ 0
Lean.Meta.Simp.instInhabitedContext.default
Lean.Meta.Tactic.Simp.Types
Lean.Meta.Simp.Context
Lean.IR.Decl.noConfusion
Lean.Compiler.IR.Basic
{P : Sort u} → {t t' : Lean.IR.Decl} → t = t' → Lean.IR.Decl.noConfusionType P t t'
Lean.Server.Watchdog.handleIleanInfoUpdate
Lean.Server.Watchdog
Lean.Server.Watchdog.FileWorker → Lean.Lsp.LeanIleanInfoParams → Lean.Server.Watchdog.ServerM Unit
LinearIsometryEquiv.toHomeomorph_injective
Mathlib.Analysis.Normed.Operator.LinearIsometry
∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂] {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [inst_2 : RingHomInvPair σ₁₂ σ₂₁] [inst_3 : RingHomInvPair σ₂₁ σ₁₂] [inst_4 : SeminormedAddCommGroup E] [inst_5 : SeminormedAddCommGroup E₂] [inst_6 : Module R E] [inst_7 : Module R₂ E₂], Function.Injective LinearIsometryEquiv.toHomeomorph
IO.FS.Metadata.modified
Init.System.IO
IO.FS.Metadata → IO.FS.SystemTime
TopologicalSpace.Opens.comap
Mathlib.Topology.Sets.Opens
{α : Type u_2} → {β : Type u_3} → [inst : TopologicalSpace α] → [inst_1 : TopologicalSpace β] → C(α, β) → FrameHom (TopologicalSpace.Opens β) (TopologicalSpace.Opens α)
Lean.Lsp.ClientCapabilities.casesOn
Lean.Data.Lsp.Capabilities
{motive : Lean.Lsp.ClientCapabilities → Sort u} → (t : Lean.Lsp.ClientCapabilities) → ((textDocument? : Option Lean.Lsp.TextDocumentClientCapabilities) → (window? : Option Lean.Lsp.WindowClientCapabilities) → (workspace? : Option Lean.Lsp.WorkspaceClientCapabilities) → (lean? : Option Lean.Lsp.LeanClientCapabilities) → motive { textDocument? := textDocument?, window? := window?, workspace? := workspace?, lean? := lean? }) → motive t
_private.Std.Time.Date.Unit.Day.0.Std.Time.Day.Offset.toMilliseconds._proof_1
Std.Time.Date.Unit.Day
86400 / ↑86400000 = 1 / 1000
LocallyConstant.comapAddMonoidHom_apply
Mathlib.Topology.LocallyConstant.Algebra
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {Z : Type u_6} [inst_2 : AddZeroClass Z] (f : C(X, Y)) (g : LocallyConstant Y Z), (LocallyConstant.comapAddMonoidHom f) g = LocallyConstant.comap f g
mul_two
Mathlib.Algebra.Ring.Defs
∀ {α : Type u} [inst : NonAssocSemiring α] (n : α), n * 2 = n + n
_private.Lean.Elab.Print.0.Lean.Elab.Command.printIdCore._sparseCasesOn_1
Lean.Elab.Print
{motive : Lean.ConstantKind → Sort u} → (t : Lean.ConstantKind) → motive Lean.ConstantKind.defn → motive Lean.ConstantKind.thm → (Nat.hasNotBit 3 t.ctorIdx → motive t) → motive t
Lean.Meta.getUInt16Value?
Lean.Meta.LitValues
Lean.Expr → Lean.MetaM (Option UInt16)
StrictMonoOn.exists_slope_lt_deriv
Mathlib.Analysis.Convex.Deriv
∀ {x y : ℝ} {f : ℝ → ℝ}, ContinuousOn f (Set.Icc x y) → x < y → StrictMonoOn (deriv f) (Set.Ioo x y) → ∃ a ∈ Set.Ioo x y, (f y - f x) / (y - x) < deriv f a
Algebra.EssFiniteType.isNoetherianRing
Mathlib.RingTheory.Localization.Submodule
∀ (R : Type u_3) (S : Type u_4) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Algebra.EssFiniteType R S] [IsNoetherianRing R], IsNoetherianRing S
MulAction.stabilizerEquivStabilizer.congr_simp
Mathlib.GroupTheory.GroupAction.Basic
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {g g_1 : G} (e_g : g = g_1) {a b : α} (hg : b = g • a), MulAction.stabilizerEquivStabilizer hg = MulAction.stabilizerEquivStabilizer ⋯
Algebra.instMulDistribMulActionAlgHomUnits._proof_2
Mathlib.Algebra.Algebra.Hom
∀ {R : Type u_2} (A : Type u_1) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : Aˣ), 1 • x = x
_private.Mathlib.Analysis.Normed.Module.FiniteDimension.0.isOpen_setOf_nat_le_rank._simp_1_1
Mathlib.Analysis.Normed.Module.FiniteDimension
∀ {K : Type u} {V : Type v} {V' : Type v'} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [inst_3 : AddCommGroup V'] [inst_4 : Module K V'] {n : ℕ} {f : V →ₗ[K] V'}, (↑n ≤ f.rank) = ∃ s, s.card = n ∧ LinearIndependent K fun (x : ↑↑s) => f ↑x
CategoryTheory.Discrete.opposite_inverse_obj
Mathlib.CategoryTheory.Discrete.Basic
∀ (α : Type u₁) (a : CategoryTheory.Discrete α), (CategoryTheory.Discrete.opposite α).inverse.obj a = Opposite.op a
CategoryTheory.Functor.Additive.map_add._autoParam
Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
Lean.Syntax
CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct
Mathlib.CategoryTheory.Bicategory.Functor.Prelax
{B : Type u₁} → [inst : CategoryTheory.Bicategory B] → {C : Type u₂} → [inst_1 : CategoryTheory.Bicategory C] → CategoryTheory.PrelaxFunctor B C → CategoryTheory.PrelaxFunctorStruct B C
IsLprojection.Subtype.BooleanAlgebra._proof_12
Mathlib.Analysis.Normed.Module.MStructure
∀ {X : Type u_2} [inst : NormedAddCommGroup X] {M : Type u_1} [inst_1 : Ring M] [inst_2 : Module M X] [inst_3 : FaithfulSMul M X] (P Q : { P // IsLprojection X P }), P \ Q = P ⊓ Qᶜ
Lean.SimplePersistentEnvExtension
Lean.EnvExtension
Type → Type → Type
hasFTaylorSeriesUpToOn_succ_iff_right
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] {s : Set E} {f : E → F} {n : WithTop ℕ∞} {p : E → FormalMultilinearSeries 𝕜 E F}, HasFTaylorSeriesUpToOn (n + 1) f p s ↔ (∀ x ∈ s, (p x 0).curry0 = f x) ∧ (∀ x ∈ s, HasFDerivWithinAt (fun y => p y 0) (p x 1).curryLeft s x) ∧ HasFTaylorSeriesUpToOn n (fun x => (continuousMultilinearCurryFin1 𝕜 E F) (p x 1)) (fun x => (p x).shift) s
Lean.Server.FileWorker.Query.noConfusion
Lean.Server.CodeActions.UnknownIdentifier
{P : Sort u} → {t t' : Lean.Server.FileWorker.Query} → t = t' → Lean.Server.FileWorker.Query.noConfusionType P t t'
MeasureTheory.eLpNorm'_congr_nnnorm_ae
Mathlib.MeasureTheory.Function.LpSeminorm.Basic
∀ {α : Type u_1} {F : Type u_5} {m0 : MeasurableSpace α} {q : ℝ} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup F] {f g : α → F}, (∀ᵐ (x : α) ∂μ, ‖f x‖₊ = ‖g x‖₊) → MeasureTheory.eLpNorm' f q μ = MeasureTheory.eLpNorm' g q μ
LinearMap.continuousAt_zero_of_locally_bounded
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded
∀ {𝕜 : Type u_1} {𝕜' : Type u_2} {E : Type u_3} {F : Type u_4} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E] [IsTopologicalAddGroup E] [inst_3 : AddCommGroup F] [inst_4 : TopologicalSpace F] [inst_5 : NontriviallyNormedField 𝕜] [inst_6 : Module 𝕜 E] [ContinuousSMul 𝕜 E] [inst_8 : NormedField 𝕜'] [inst_9 : Module 𝕜' F] {σ : 𝕜 →+* 𝕜'} [RingHomIsometric σ] [FirstCountableTopology E] (f : E →ₛₗ[σ] F), (∀ (s : Set E), Bornology.IsVonNBounded 𝕜 s → Bornology.IsVonNBounded 𝕜' (⇑f '' s)) → ContinuousAt (⇑f) 0
Lean.Elab.Tactic.BVDecide.Frontend.UnsatProver.Result.mk.sizeOf_spec
Lean.Elab.Tactic.BVDecide.Frontend.BVDecide
∀ (proof : Lean.Expr) (lratCert : Lean.Elab.Tactic.BVDecide.Frontend.LratCert), sizeOf { proof := proof, lratCert := lratCert } = 1 + sizeOf proof + sizeOf lratCert
DistribMulActionHom.rec
Mathlib.GroupTheory.GroupAction.Hom
{M : Type u_1} → [inst : Monoid M] → {N : Type u_2} → [inst_1 : Monoid N] → {φ : M →* N} → {A : Type u_4} → [inst_2 : AddMonoid A] → [inst_3 : DistribMulAction M A] → {B : Type u_5} → [inst_4 : AddMonoid B] → [inst_5 : DistribMulAction N B] → {motive : (A →ₑ+[φ] B) → Sort u} → ((toMulActionHom : A →ₑ[⇑φ] B) → (map_zero' : toMulActionHom.toFun 0 = 0) → (map_add' : ∀ (x y : A), toMulActionHom.toFun (x + y) = toMulActionHom.toFun x + toMulActionHom.toFun y) → motive { toMulActionHom := toMulActionHom, map_zero' := map_zero', map_add' := map_add' }) → (t : A →ₑ+[φ] B) → motive t
MonadCont.Label.noConfusion
Mathlib.Control.Monad.Cont
{P : Sort u_1} → {α : Type w} → {m : Type u → Type v} → {β : Type u} → {t : MonadCont.Label α m β} → {α' : Type w} → {m' : Type u → Type v} → {β' : Type u} → {t' : MonadCont.Label α' m' β'} → α = α' → m = m' → β = β' → t ≍ t' → MonadCont.Label.noConfusionType P t t'
RightOrdContinuous.toOrderEmbedding
Mathlib.Order.OrdContinuous
{α : Type u} → {β : Type v} → [inst : SemilatticeInf α] → [inst_1 : SemilatticeInf β] → (f : α → β) → RightOrdContinuous f → Function.Injective f → α ↪o β
Aesop.GoalData.mk.sizeOf_spec
Aesop.Tree.Data
∀ {Rapp MVarCluster : Type} [inst : SizeOf Rapp] [inst_1 : SizeOf MVarCluster] (id : Aesop.GoalId) (parent : IO.Ref MVarCluster) (children : Array (IO.Ref Rapp)) (origin : Aesop.GoalOrigin) (depth : ℕ) (state : Aesop.GoalState) (isIrrelevant isForcedUnprovable : Bool) (preNormGoal : Lean.MVarId) (normalizationState : Aesop.NormalizationState) (mvars : Aesop.UnorderedArraySet Lean.MVarId) (forwardState : Aesop.ForwardState) (forwardRuleMatches : Aesop.ForwardRuleMatches) (successProbability : Aesop.Percent) (addedInIteration lastExpandedInIteration : Aesop.Iteration) (unsafeRulesSelected : Bool) (unsafeQueue : Aesop.UnsafeQueue) (failedRapps : Array Aesop.RegularRule), sizeOf { id := id, parent := parent, children := children, origin := origin, depth := depth, state := state, isIrrelevant := isIrrelevant, isForcedUnprovable := isForcedUnprovable, preNormGoal := preNormGoal, normalizationState := normalizationState, mvars := mvars, forwardState := forwardState, forwardRuleMatches := forwardRuleMatches, successProbability := successProbability, addedInIteration := addedInIteration, lastExpandedInIteration := lastExpandedInIteration, unsafeRulesSelected := unsafeRulesSelected, unsafeQueue := unsafeQueue, failedRapps := failedRapps } = 1 + sizeOf id + sizeOf parent + sizeOf children + sizeOf origin + sizeOf depth + sizeOf state + sizeOf isIrrelevant + sizeOf isForcedUnprovable + sizeOf preNormGoal + sizeOf normalizationState + sizeOf mvars + sizeOf forwardState + sizeOf forwardRuleMatches + sizeOf successProbability + sizeOf addedInIteration + sizeOf lastExpandedInIteration + sizeOf unsafeRulesSelected + sizeOf unsafeQueue + sizeOf failedRapps
Complex.tan_add_int_mul_pi
Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
∀ (x : ℂ) (n : ℤ), Complex.tan (x + ↑n * ↑Real.pi) = Complex.tan x
AddQuantale.rec
Mathlib.Algebra.Order.Quantale
{α : Type u_1} → [inst : AddSemigroup α] → [inst_1 : CompleteLattice α] → [inst_2 : IsAddQuantale α] → {motive : AddQuantale α → Sort u} → motive { } → (t : AddQuantale α) → motive t
MeasurableSpace.GenerateMeasurable.below.compl
Mathlib.MeasureTheory.MeasurableSpace.Defs
∀ {α : Type u_1} {s : Set (Set α)} {motive : (a : Set α) → MeasurableSpace.GenerateMeasurable s a → Prop} (t : Set α) (a : MeasurableSpace.GenerateMeasurable s t), MeasurableSpace.GenerateMeasurable.below a → motive t a → MeasurableSpace.GenerateMeasurable.below ⋯
Lean.ParserDescr.recOn
Init.Prelude
{motive : Lean.ParserDescr → Sort u} → (t : Lean.ParserDescr) → ((name : Lean.Name) → motive (Lean.ParserDescr.const name)) → ((name : Lean.Name) → (p : Lean.ParserDescr) → motive p → motive (Lean.ParserDescr.unary name p)) → ((name : Lean.Name) → (p₁ p₂ : Lean.ParserDescr) → motive p₁ → motive p₂ → motive (Lean.ParserDescr.binary name p₁ p₂)) → ((kind : Lean.SyntaxNodeKind) → (prec : ℕ) → (p : Lean.ParserDescr) → motive p → motive (Lean.ParserDescr.node kind prec p)) → ((kind : Lean.SyntaxNodeKind) → (prec lhsPrec : ℕ) → (p : Lean.ParserDescr) → motive p → motive (Lean.ParserDescr.trailingNode kind prec lhsPrec p)) → ((val : String) → motive (Lean.ParserDescr.symbol val)) → ((val : String) → (includeIdent : Bool) → motive (Lean.ParserDescr.nonReservedSymbol val includeIdent)) → ((catName : Lean.Name) → (rbp : ℕ) → motive (Lean.ParserDescr.cat catName rbp)) → ((declName : Lean.Name) → motive (Lean.ParserDescr.parser declName)) → ((name : String) → (kind : Lean.SyntaxNodeKind) → (p : Lean.ParserDescr) → motive p → motive (Lean.ParserDescr.nodeWithAntiquot name kind p)) → ((p : Lean.ParserDescr) → (sep : String) → (psep : Lean.ParserDescr) → (allowTrailingSep : Bool) → motive p → motive psep → motive (p.sepBy sep psep allowTrailingSep)) → ((p : Lean.ParserDescr) → (sep : String) → (psep : Lean.ParserDescr) → (allowTrailingSep : Bool) → motive p → motive psep → motive (p.sepBy1 sep psep allowTrailingSep)) → ((val asciiVal : String) → (preserveForPP : Bool) → motive (Lean.ParserDescr.unicodeSymbol val asciiVal preserveForPP)) → motive t
ISize.reduceToInt._regBuiltin.ISize.reduceToInt.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.2118279935._hygCtx._hyg.15
Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt
IO Unit
FormalMultilinearSeries.restrictScalars.congr_simp
Mathlib.Analysis.Analytic.Binomial
∀ (𝕜 : Type u) {𝕜' : Type u'} {E : Type v} {F : Type w} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : Module 𝕜 E] [inst_3 : TopologicalSpace E] [inst_4 : ContinuousAdd E] [inst_5 : ContinuousConstSMul 𝕜 E] [inst_6 : AddCommMonoid F] [inst_7 : Module 𝕜 F] [inst_8 : TopologicalSpace F] [inst_9 : ContinuousAdd F] [inst_10 : ContinuousConstSMul 𝕜 F] [inst_11 : Semiring 𝕜'] [inst_12 : SMul 𝕜 𝕜'] [inst_13 : Module 𝕜' E] [inst_14 : ContinuousConstSMul 𝕜' E] [inst_15 : IsScalarTower 𝕜 𝕜' E] [inst_16 : Module 𝕜' F] [inst_17 : ContinuousConstSMul 𝕜' F] [inst_18 : IsScalarTower 𝕜 𝕜' F] (p p_1 : FormalMultilinearSeries 𝕜' E F), p = p_1 → ∀ (n : ℕ), FormalMultilinearSeries.restrictScalars 𝕜 p n = FormalMultilinearSeries.restrictScalars 𝕜 p_1 n
Std.Sat.AIG.RefVec.fold.congr_simp
Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Eq
∀ {α : Type} [inst : Hashable α] [inst_1 : DecidableEq α] {len : ℕ} (aig : Std.Sat.AIG α) (vec vec_1 : aig.RefVec len), vec = vec_1 → ∀ (func func_1 : (aig : Std.Sat.AIG α) → aig.BinaryInput → Std.Sat.AIG.Entrypoint α) (e_func : func = func_1) [inst_2 : Std.Sat.AIG.LawfulOperator α Std.Sat.AIG.BinaryInput func], Std.Sat.AIG.RefVec.fold aig vec func = Std.Sat.AIG.RefVec.fold aig vec_1 func_1
Mathlib.Tactic.LinearCombination'.Expanded.noConfusionType
Mathlib.Tactic.LinearCombination'
Sort u → Mathlib.Tactic.LinearCombination'.Expanded → Mathlib.Tactic.LinearCombination'.Expanded → Sort u
_private.Mathlib.LinearAlgebra.Eigenspace.Zero.0.LinearMap.hasEigenvalue_zero_tfae.match_1_6
Mathlib.LinearAlgebra.Eigenspace.Zero
∀ {K : Type u_2} {M : Type u_1} [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M] (φ : Module.End K M) (motive : (∃ m, m ≠ 0 ∧ φ m = 0) → Prop) (x : ∃ m, m ≠ 0 ∧ φ m = 0), (∀ (x : M) (h1 : x ≠ 0) (h2 : φ x = 0), motive ⋯) → motive x
_private.Lean.Elab.Tactic.Conv.Congr.0.Lean.Elab.Tactic.Conv.mkCongrThm.match_1
Lean.Elab.Tactic.Conv.Congr
(motive : Lean.Expr × Lean.Expr → Sort u_1) → (__discr : Lean.Expr × Lean.Expr) → ((rhs mvarNew : Lean.Expr) → motive (rhs, mvarNew)) → motive __discr
Std.Tactic.BVDecide.LRAT.Internal.Formula.readyForRatAdd_insert
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), Std.Tactic.BVDecide.LRAT.Internal.Formula.ReadyForRatAdd f → Std.Tactic.BVDecide.LRAT.Internal.Formula.ReadyForRatAdd (Std.Tactic.BVDecide.LRAT.Internal.Formula.insert f c)
ContextFreeGrammar.Generates.eq_1
Mathlib.Computability.ContextFreeGrammar
∀ {T : Type u_1} (g : ContextFreeGrammar T) (s : List (Symbol T g.NT)), g.Generates s = g.Derives [Symbol.nonterminal g.initial] s
AlgebraicGeometry.smoothOfRelativeDimension_comp
Mathlib.AlgebraicGeometry.Morphisms.Smooth
∀ (n m : ℕ) {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {Z : AlgebraicGeometry.Scheme} (g : Y ⟶ Z) [hf : AlgebraicGeometry.SmoothOfRelativeDimension n f] [hg : AlgebraicGeometry.SmoothOfRelativeDimension m g], AlgebraicGeometry.SmoothOfRelativeDimension (n + m) (CategoryTheory.CategoryStruct.comp f g)
TensorProduct.AlgebraTensorModule.ext
Mathlib.LinearAlgebra.TensorProduct.Tower
∀ {R : Type uR} {A : Type uA} {M : Type uM} {N : Type uN} {P : Type uP} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module A M] [inst_6 : IsScalarTower R A M] [inst_7 : AddCommMonoid N] [inst_8 : Module R N] [inst_9 : AddCommMonoid P] [inst_10 : Module R P] [inst_11 : Module A P] [IsScalarTower R A P] {g h : TensorProduct R M N →ₗ[A] P}, (∀ (x : M) (y : N), g (x ⊗ₜ[R] y) = h (x ⊗ₜ[R] y)) → g = h
Lean.Lsp.TextDocumentContentChangeEvent.rec
Lean.Data.Lsp.TextSync
{motive : Lean.Lsp.TextDocumentContentChangeEvent → Sort u} → ((range : Lean.Lsp.Range) → (text : String) → motive (Lean.Lsp.TextDocumentContentChangeEvent.rangeChange range text)) → ((text : String) → motive (Lean.Lsp.TextDocumentContentChangeEvent.fullChange text)) → (t : Lean.Lsp.TextDocumentContentChangeEvent) → motive t
_private.Mathlib.Data.Nat.Bits.0.Nat.bodd_eq_one_and_ne_zero.match_1_1
Mathlib.Data.Nat.Bits
∀ (motive : ℕ → Prop) (x : ℕ), (∀ (a : Unit), motive 0) → (∀ (a : Unit), motive 1) → (∀ (n : ℕ), motive n.succ.succ) → motive x
SimpleGraph.Walk.adj_snd._simp_1
Mathlib.Combinatorics.SimpleGraph.Walks.Traversal
∀ {V : Type u} {G : SimpleGraph V} {v w : V} {p : G.Walk v w}, ¬p.Nil → G.1 v p.snd = True
AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd
Mathlib.AlgebraicGeometry.PullbackCarrier
∀ {X Y S : AlgebraicGeometry.Scheme} {f : X ⟶ S} {g : Y ⟶ S} (T : AlgebraicGeometry.Scheme.Pullback.Triplet f g) (p : ↥(AlgebraicGeometry.Spec T.tensor)), (CategoryTheory.Limits.pullback.snd f g) (T.SpecTensorTo p) = T.y
FloorSemiring.mk
Mathlib.Algebra.Order.Floor.Defs
{α : Type u_4} → [inst : Semiring α] → [inst_1 : PartialOrder α] → (floor ceil : α → ℕ) → (∀ {a : α}, a < 0 → floor a = 0) → (∀ {a : α} {n : ℕ}, 0 ≤ a → (n ≤ floor a ↔ ↑n ≤ a)) → GaloisConnection ceil Nat.cast → FloorSemiring α
SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv
Mathlib.Analysis.Distribution.SchwartzSpace.Deriv
∀ {E : Type u_5} {F : Type u_8} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ F] [inst_3 : NormedSpace ℝ E] {n : ℕ} {m : Fin n → E} {f : SchwartzMap E F} {x : E}, (LineDeriv.iteratedLineDerivOp m f) x = (iteratedFDeriv ℝ n (⇑f) x) m
CategoryTheory.MorphismProperty.IsStableUnderFilteredColimits.mk._flat_ctor
Mathlib.CategoryTheory.MorphismProperty.Limits
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W : CategoryTheory.MorphismProperty C}, autoParam (∀ (J : Type w') [inst_1 : CategoryTheory.Category.{w, w'} J] [CategoryTheory.IsFiltered J], W.IsStableUnderColimitsOfShape J) CategoryTheory.MorphismProperty.IsStableUnderFilteredColimits.isStableUnderColimitsOfShape._autoParam → CategoryTheory.MorphismProperty.IsStableUnderFilteredColimits.{w, w', v, u} W