File: Mathlib/Order/Notation.lean

full_name: HasCompl
code: /-- Set / lattice complement -/
@[notation_class]
class HasCompl (α : Type*) where
  /-- Set / lattice complement -/
  compl : α → α
goal: Type u_1

full_name: HasCompl.compl
code: /-- Set / lattice complement -/
@[notation_class]
class HasCompl (α : Type*) where
  /-- Set / lattice complement -/
  compl : α → α
goal: α → α

full_name: «_aux_Mathlib_Order_Notation___macroRules_term_ᶜ_1»
code: @[inherit_doc]
postfix:1024 "ᶜ" => compl
goal: Lean.Macro

full_name: _aux_Mathlib_Order_Notation___unexpand_HasCompl_compl_1
code: @[inherit_doc]
postfix:1024 "ᶜ" => compl
goal: Lean.PrettyPrinter.Unexpander

full_name: Sup.sup
code: /-- Typeclass for the `⊔` (`\lub`) notation -/
@[notation_class, ext]
class Sup (α : Type*) where
  /-- Least upper bound (`\lub` notation) -/
  sup : α → α → α
goal: α → α → α

full_name: Sup
code: /-- Typeclass for the `⊔` (`\lub`) notation -/
@[notation_class, ext]
class Sup (α : Type*) where
  /-- Least upper bound (`\lub` notation) -/
  sup : α → α → α
goal: Type u_1

full_name: Inf.inf
code: /-- Typeclass for the `⊓` (`\glb`) notation -/
@[notation_class, ext]
class Inf (α : Type*) where
  /-- Greatest lower bound (`\glb` notation) -/
  inf : α → α → α
goal: α → α → α

full_name: Inf
code: /-- Typeclass for the `⊓` (`\glb`) notation -/
@[notation_class, ext]
class Inf (α : Type*) where
  /-- Greatest lower bound (`\glb` notation) -/
  inf : α → α → α
goal: Type u_1

full_name: _aux_Mathlib_Order_Notation___unexpand_Sup_sup_1
code: @[inherit_doc]
infixl:68 " ⊔ " => Sup.sup
goal: Lean.PrettyPrinter.Unexpander

full_name: «_aux_Mathlib_Order_Notation___macroRules_term_⊔__1»
code: @[inherit_doc]
infixl:68 " ⊔ " => Sup.sup
goal: Lean.Macro

full_name: «_aux_Mathlib_Order_Notation___macroRules_term_⊓__1»
code: @[inherit_doc]
infixl:69 " ⊓ " => Inf.inf
goal: Lean.Macro

full_name: _aux_Mathlib_Order_Notation___unexpand_Inf_inf_1
code: @[inherit_doc]
infixl:69 " ⊓ " => Inf.inf
goal: Lean.PrettyPrinter.Unexpander

full_name: HImp
code: /-- Syntax typeclass for Heyting implication `⇨`. -/
@[notation_class]
class HImp (α : Type*) where
  /-- Heyting implication `⇨` -/
  himp : α → α → α
goal: Type u_1

full_name: HImp.himp
code: /-- Syntax typeclass for Heyting implication `⇨`. -/
@[notation_class]
class HImp (α : Type*) where
  /-- Heyting implication `⇨` -/
  himp : α → α → α
goal: α → α → α

full_name: HNot.hnot
code: /-- Syntax typeclass for Heyting negation `￢`.

The difference between `HasCompl` and `HNot` is that the former belongs to Heyting algebras,
while the latter belongs to co-Heyting algebras. They are both pseudo-complements, but `compl`
underestimates while `HNot` overestimates. In boolean algebras, they are equal.
See `hnot_eq_compl`.
-/
@[notation_class]
class HNot (α : Type*) where
  /-- Heyting negation `￢` -/
  hnot : α → α
goal: α → α

full_name: HNot
code: /-- Syntax typeclass for Heyting negation `￢`.

The difference between `HasCompl` and `HNot` is that the former belongs to Heyting algebras,
while the latter belongs to co-Heyting algebras. They are both pseudo-complements, but `compl`
underestimates while `HNot` overestimates. In boolean algebras, they are equal.
See `hnot_eq_compl`.
-/
@[notation_class]
class HNot (α : Type*) where
  /-- Heyting negation `￢` -/
  hnot : α → α
goal: Type u_1

full_name: _aux_Mathlib_Order_Notation___unexpand_HImp_himp_1
code: /-- Heyting implication -/
infixr:60 " ⇨ " => himp
goal: Lean.PrettyPrinter.Unexpander

full_name: «_aux_Mathlib_Order_Notation___macroRules_term_⇨__1»
code: /-- Heyting implication -/
infixr:60 " ⇨ " => himp
goal: Lean.Macro

full_name: _aux_Mathlib_Order_Notation___unexpand_HNot_hnot_1
code: /-- Heyting negation -/
prefix:72 "￢" => hnot
goal: Lean.PrettyPrinter.Unexpander

full_name: «_aux_Mathlib_Order_Notation___macroRules_term￢__1»
code: /-- Heyting negation -/
prefix:72 "￢" => hnot
goal: Lean.Macro

full_name: Top.top
code: /-- Typeclass for the `⊤` (`\top`) notation -/
@[notation_class, ext]
class Top (α : Type*) where
  /-- The top (`⊤`, `\top`) element -/
  top : α
goal: α

full_name: Top
code: /-- Typeclass for the `⊤` (`\top`) notation -/
@[notation_class, ext]
class Top (α : Type*) where
  /-- The top (`⊤`, `\top`) element -/
  top : α
goal: Type u_1

full_name: Bot.bot
code: /-- Typeclass for the `⊥` (`\bot`) notation -/
@[notation_class, ext]
class Bot (α : Type*) where
  /-- The bot (`⊥`, `\bot`) element -/
  bot : α
goal: α

full_name: Bot
code: /-- Typeclass for the `⊥` (`\bot`) notation -/
@[notation_class, ext]
class Bot (α : Type*) where
  /-- The bot (`⊥`, `\bot`) element -/
  bot : α
goal: Type u_1

full_name: _aux_Mathlib_Order_Notation___unexpand_Top_top_1
code: /-- The top (`⊤`, `\top`) element -/
notation "⊤" => Top.top
goal: Lean.PrettyPrinter.Unexpander

full_name: «_aux_Mathlib_Order_Notation___macroRules_term⊤_1»
code: /-- The top (`⊤`, `\top`) element -/
notation "⊤" => Top.top
goal: Lean.Macro

full_name: «_aux_Mathlib_Order_Notation___macroRules_term⊥_1»
code: /-- The bot (`⊥`, `\bot`) element -/
notation "⊥" => Bot.bot
goal: Lean.Macro

full_name: _aux_Mathlib_Order_Notation___unexpand_Bot_bot_1
code: /-- The bot (`⊥`, `\bot`) element -/
notation "⊥" => Bot.bot
goal: Lean.PrettyPrinter.Unexpander

full_name: top_nonempty
code: instance (priority := 100) top_nonempty (α : Type*) [Top α] : Nonempty α 
goal: Nonempty α

full_name: bot_nonempty
code: instance (priority := 100) bot_nonempty (α : Type*) [Bot α] : Nonempty α 
goal: Nonempty α