File: Mathlib/Order/SetNotation.lean

full_name: SupSet.sSup
code: /-- Class for the `sSup` operator -/
class SupSet (α : Type*) where
  /-- Supremum of a set -/
  sSup : Set α → α
goal: Set α → α

full_name: SupSet
code: /-- Class for the `sSup` operator -/
class SupSet (α : Type*) where
  /-- Supremum of a set -/
  sSup : Set α → α
goal: Type u_1

full_name: InfSet
code: /-- Class for the `sInf` operator -/
class InfSet (α : Type*) where
  /-- Infimum of a set -/
  sInf : Set α → α
goal: Type u_1

full_name: InfSet.sInf
code: /-- Class for the `sInf` operator -/
class InfSet (α : Type*) where
  /-- Infimum of a set -/
  sInf : Set α → α
goal: Set α → α

full_name: iSup
code: /-- Indexed supremum -/
def iSup [SupSet α] (s : ι → α) : α 
goal: α

full_name: iInf
code: /-- Indexed infimum -/
def iInf [InfSet α] (s : ι → α) : α 
goal: α

full_name: infSet_to_nonempty
code: instance (priority := 50) infSet_to_nonempty (α) [InfSet α] : Nonempty α 
goal: Nonempty α

full_name: supSet_to_nonempty
code: instance (priority := 50) supSet_to_nonempty (α) [SupSet α] : Nonempty α 
goal: Nonempty α

full_name: «_aux_Mathlib_Order_SetNotation___macroRules_term⨆_,__1»
code: /-- Indexed supremum. -/
notation3 "⨆ "(...)", "r:60:(scoped f => iSup f) => r
goal: Lean.Macro

full_name: «_aux_Mathlib_Order_SetNotation___macroRules_term⨅_,__1»
code: /-- Indexed infimum. -/
notation3 "⨅ "(...)", "r:60:(scoped f => iInf f) => r
goal: Lean.Macro

full_name: iSup_delab
code: /-- Delaborator for indexed supremum. -/
@[delab app.iSup]
def iSup_delab : Delab 
goal: Lean.PrettyPrinter.Delaborator.Delab

full_name: iInf_delab
code: /-- Delaborator for indexed infimum. -/
@[delab app.iInf]
def iInf_delab : Delab 
goal: Lean.PrettyPrinter.Delaborator.Delab

full_name: Set.instInfSet
code: instance : InfSet (Set α) 
goal: InfSet (Set α)

full_name: Set.instSupSet
code: instance : SupSet (Set α) 
goal: SupSet (Set α)

full_name: Set.sInter
code: /-- Intersection of a set of sets. -/
def sInter (S : Set (Set α)) : Set α 
goal: Set α

full_name: Set.«_aux_Mathlib_Order_SetNotation___macroRules_Set_term⋂₀__1»
code: /-- Notation for `Set.sInter` Intersection of a set of sets. -/
prefix:110 "⋂₀ " => sInter
goal: Lean.Macro

full_name: Set._aux_Mathlib_Order_SetNotation___unexpand_Set_sInter_1
code: /-- Notation for `Set.sInter` Intersection of a set of sets. -/
prefix:110 "⋂₀ " => sInter
goal: Lean.PrettyPrinter.Unexpander

full_name: Set.sUnion
code: /-- Union of a set of sets. -/
def sUnion (S : Set (Set α)) : Set α 
goal: Set α

full_name: Set._aux_Mathlib_Order_SetNotation___unexpand_Set_sUnion_1
code: /-- Notation for `Set.sUnion`. Union of a set of sets. -/
prefix:110 "⋃₀ " => sUnion
goal: Lean.PrettyPrinter.Unexpander

full_name: Set.«_aux_Mathlib_Order_SetNotation___macroRules_Set_term⋃₀__1»
code: /-- Notation for `Set.sUnion`. Union of a set of sets. -/
prefix:110 "⋃₀ " => sUnion
goal: Lean.Macro

full_name: Set.mem_sInter
code: @[simp]
theorem mem_sInter {x : α} {S : Set (Set α)} : x ∈ ⋂₀ S ↔ ∀ t ∈ S, x ∈ t 
goal: x ∈ ⋂₀ S ↔ ∀ (t : Set α), t ∈ S → x ∈ t

full_name: Set.mem_sUnion
code: @[simp]
theorem mem_sUnion {x : α} {S : Set (Set α)} : x ∈ ⋃₀ S ↔ ∃ t ∈ S, x ∈ t 
goal: x ∈ ⋃₀ S ↔ ∃ t, t ∈ S ∧ x ∈ t

full_name: Set.iUnion
code: /-- Indexed union of a family of sets -/
def iUnion (s : ι → Set α) : Set α 
goal: Set α

full_name: Set.iInter
code: /-- Indexed intersection of a family of sets -/
def iInter (s : ι → Set α) : Set α 
goal: Set α

full_name: Set.«_aux_Mathlib_Order_SetNotation___macroRules_Set_term⋃_,__1»
code: /-- Notation for `Set.iUnion`. Indexed union of a family of sets -/
notation3 "⋃ "(...)", "r:60:(scoped f => iUnion f) => r
goal: Lean.Macro

full_name: Set.«_aux_Mathlib_Order_SetNotation___macroRules_Set_term⋂_,__1»
code: /-- Notation for `Set.iInter`. Indexed intersection of a family of sets -/
notation3 "⋂ "(...)", "r:60:(scoped f => iInter f) => r
goal: Lean.Macro

full_name: Set.iUnion_delab
code: /-- Delaborator for indexed unions. -/
@[delab app.Set.iUnion]
def iUnion_delab : Delab 
goal: Lean.PrettyPrinter.Delaborator.Delab

full_name: Set.sInter_delab
code: /-- Delaborator for indexed intersections. -/
@[delab app.Set.iInter]
def sInter_delab : Delab 
goal: Lean.PrettyPrinter.Delaborator.Delab

full_name: Set.mem_iUnion
code: @[simp]
theorem mem_iUnion {x : α} {s : ι → Set α} : (x ∈ ⋃ i, s i) ↔ ∃ i, x ∈ s i 
goal: x ∈ ⋃ i, s i ↔ ∃ i, x ∈ s i

full_name: Set.mem_iInter
code: @[simp]
theorem mem_iInter {x : α} {s : ι → Set α} : (x ∈ ⋂ i, s i) ↔ ∀ i, x ∈ s i 
goal: x ∈ ⋂ i, s i ↔ ∀ (i : ι), x ∈ s i

full_name: Set.sSup_eq_sUnion
code: @[simp]
theorem sSup_eq_sUnion (S : Set (Set α)) : sSup S = ⋃₀S 
goal: sSup S = ⋃₀ S

full_name: Set.sInf_eq_sInter
code: @[simp]
theorem sInf_eq_sInter (S : Set (Set α)) : sInf S = ⋂₀ S 
goal: sInf S = ⋂₀ S

full_name: Set.iSup_eq_iUnion
code: @[simp]
theorem iSup_eq_iUnion (s : ι → Set α) : iSup s = iUnion s 
goal: iSup s = Set.iUnion s

full_name: Set.iInf_eq_iInter
code: @[simp]
theorem iInf_eq_iInter (s : ι → Set α) : iInf s = iInter s 
goal: iInf s = Set.iInter s