File: Mathlib/Order/Category/BddDistLat.lean

full_name: BddDistLat.isBoundedOrder
code: /-- The category of bounded distributive lattices with bounded lattice morphisms. -/
structure BddDistLat where
  /-- The underlying distrib lattice of a bounded distributive lattice. -/
  toDistLat : DistLat
  [isBoundedOrder : BoundedOrder toDistLat]
goal: BoundedOrder ↑self.toDistLat

full_name: BddDistLat
code: /-- The category of bounded distributive lattices with bounded lattice morphisms. -/
structure BddDistLat where
  /-- The underlying distrib lattice of a bounded distributive lattice. -/
  toDistLat : DistLat
  [isBoundedOrder : BoundedOrder toDistLat]
goal: Type (u_1 + 1)

full_name: BddDistLat.toDistLat
code: /-- The category of bounded distributive lattices with bounded lattice morphisms. -/
structure BddDistLat where
  /-- The underlying distrib lattice of a bounded distributive lattice. -/
  toDistLat : DistLat
  [isBoundedOrder : BoundedOrder toDistLat]
goal: DistLat

full_name: BddDistLat.instCoeSortType
code: instance : CoeSort BddDistLat Type* 
goal: CoeSort BddDistLat (Type u_1)

full_name: BddDistLat.instDistribLatticeαToDistLat
code: instance (X : BddDistLat) : DistribLattice X 
goal: DistribLattice ↑X.toDistLat

full_name: BddDistLat.of
code: /-- Construct a bundled `BddDistLat` from a `BoundedOrder` `DistribLattice`. -/
def of (α : Type*) [DistribLattice α] [BoundedOrder α] : BddDistLat 
goal: BddDistLat

full_name: BddDistLat.coe_of
code: @[simp]
theorem coe_of (α : Type*) [DistribLattice α] [BoundedOrder α] : ↥(of α) = α 
goal: ↑(BddDistLat.of α).toDistLat = α

full_name: BddDistLat.instInhabited
code: instance : Inhabited BddDistLat 
goal: Inhabited BddDistLat

full_name: BddDistLat.toBddLat
code: /-- Turn a `BddDistLat` into a `BddLat` by forgetting it is distributive. -/
def toBddLat (X : BddDistLat) : BddLat 
goal: BddLat

full_name: BddDistLat.coe_toBddLat
code: @[simp]
theorem coe_toBddLat (X : BddDistLat) : ↥X.toBddLat = ↥X 
goal: ↑X.toBddLat.toLat = ↑X.toDistLat

full_name: BddDistLat.instLargeCategory
code: instance : LargeCategory.{u} BddDistLat 
goal: CategoryTheory.LargeCategory BddDistLat

full_name: BddDistLat.instConcreteCategory
code: instance : ConcreteCategory BddDistLat 
goal: CategoryTheory.ConcreteCategory BddDistLat

full_name: BddDistLat.hasForgetToDistLat
code: instance hasForgetToDistLat : HasForget₂ BddDistLat DistLat 
goal: CategoryTheory.HasForget₂ BddDistLat DistLat

full_name: BddDistLat.hasForgetToBddLat
code: instance hasForgetToBddLat : HasForget₂ BddDistLat BddLat 
goal: CategoryTheory.HasForget₂ BddDistLat BddLat

full_name: BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat
code: theorem forget_bddLat_lat_eq_forget_distLat_lat :
    forget₂ BddDistLat BddLat ⋙ forget₂ BddLat Lat =
      forget₂ BddDistLat DistLat ⋙ forget₂ DistLat Lat 
goal: CategoryTheory.forget₂ BddDistLat BddLat ⋙ CategoryTheory.forget₂ BddLat Lat =
  CategoryTheory.forget₂ BddDistLat DistLat ⋙ CategoryTheory.forget₂ DistLat Lat

full_name: BddDistLat.Iso.mk
code: /-- Constructs an equivalence between bounded distributive lattices from an order isomorphism
between them. -/
@[simps]
def Iso.mk {α β : BddDistLat.{u}} (e : α ≃o β) : α ≅ β 
goal: α ≅ β

full_name: BddDistLat.Iso.mk_inv_toLatticeHom_toSupHom_toFun
code: /-- Constructs an equivalence between bounded distributive lattices from an order isomorphism
between them. -/
@[simps]
def Iso.mk {α β : BddDistLat.{u}} (e : α ≃o β) : α ≅ β 
goal: (BddDistLat.Iso.mk e).inv.toSupHom a = e.symm a

full_name: BddDistLat.Iso.mk_hom_toLatticeHom_toSupHom_toFun
code: /-- Constructs an equivalence between bounded distributive lattices from an order isomorphism
between them. -/
@[simps]
def Iso.mk {α β : BddDistLat.{u}} (e : α ≃o β) : α ≅ β 
goal: (BddDistLat.Iso.mk e).hom.toSupHom a = e a

full_name: BddDistLat.dual_map
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddDistLat ⥤ BddDistLat 
goal: BddDistLat.dual.map a = BoundedLatticeHom.dual a

full_name: BddDistLat.dual_obj
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddDistLat ⥤ BddDistLat 
goal: BddDistLat.dual.obj X = BddDistLat.of (↑X.toDistLat)ᵒᵈ

full_name: BddDistLat.dual
code: /-- `OrderDual` as a functor. -/
@[simps]
def dual : BddDistLat ⥤ BddDistLat 
goal: BddDistLat ⥤ BddDistLat

full_name: BddDistLat.dualEquiv
code: /-- The equivalence between `BddDistLat` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddDistLat ≌ BddDistLat 
goal: BddDistLat ≌ BddDistLat

full_name: BddDistLat.dualEquiv_inverse
code: /-- The equivalence between `BddDistLat` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddDistLat ≌ BddDistLat 
goal: BddDistLat.dualEquiv.inverse = BddDistLat.dual

full_name: BddDistLat.dualEquiv_functor
code: /-- The equivalence between `BddDistLat` and itself induced by `OrderDual` both ways. -/
@[simps functor inverse]
def dualEquiv : BddDistLat ≌ BddDistLat 
goal: BddDistLat.dualEquiv.functor = BddDistLat.dual

full_name: bddDistLat_dual_comp_forget_to_distLat
code: theorem bddDistLat_dual_comp_forget_to_distLat :
    BddDistLat.dual ⋙ forget₂ BddDistLat DistLat =
      forget₂ BddDistLat DistLat ⋙ DistLat.dual 
goal: BddDistLat.dual ⋙ CategoryTheory.forget₂ BddDistLat DistLat = CategoryTheory.forget₂ BddDistLat DistLat ⋙ DistLat.dual