File: Mathlib/Algebra/Category/BoolRing.lean

full_name: BoolRing
code: /-- The category of Boolean rings. -/
def BoolRing 
goal: Type (u_1 + 1)

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

full_name: BoolRing.instBooleanRingα
code: instance (X : BoolRing) : BooleanRing X 
goal: BooleanRing ↑X

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

full_name: BoolRing.coe_of
code: @[simp]
theorem coe_of (α : Type*) [BooleanRing α] : ↥(of α) = α 
goal: ↑(BoolRing.of α) = α

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

full_name: BoolRing.instParentProjectionCommRingBooleanRingToCommRing
code: instance : BundledHom.ParentProjection @BooleanRing.toCommRing 
goal: CategoryTheory.BundledHom.ParentProjection @BooleanRing.toCommRing

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

full_name: BoolRing.hasForgetToCommRing
code: instance hasForgetToCommRing : HasForget₂ BoolRing CommRingCat 
goal: CategoryTheory.HasForget₂ BoolRing CommRingCat

full_name: BoolRing.Iso.mk
code: /-- Constructs an isomorphism of Boolean rings from a ring isomorphism between them. -/
@[simps]
def Iso.mk {α β : BoolRing.{u}} (e : α ≃+* β) : α ≅ β 
goal: α ≅ β

full_name: BoolRing.Iso.mk_hom
code: /-- Constructs an isomorphism of Boolean rings from a ring isomorphism between them. -/
@[simps]
def Iso.mk {α β : BoolRing.{u}} (e : α ≃+* β) : α ≅ β 
goal: (BoolRing.Iso.mk e).hom = ↑e

full_name: BoolRing.Iso.mk_inv
code: /-- Constructs an isomorphism of Boolean rings from a ring isomorphism between them. -/
@[simps]
def Iso.mk {α β : BoolRing.{u}} (e : α ≃+* β) : α ≅ β 
goal: (BoolRing.Iso.mk e).inv = ↑e.symm

full_name: BoolRing.hasForgetToBoolAlg
code: @[simps]
instance BoolRing.hasForgetToBoolAlg : HasForget₂ BoolRing BoolAlg 
goal: CategoryTheory.HasForget₂ BoolRing BoolAlg

full_name: BoolRing.hasForgetToBoolAlg_forget₂_map
code: @[simps]
instance BoolRing.hasForgetToBoolAlg : HasForget₂ BoolRing BoolAlg 
goal: CategoryTheory.HasForget₂.forget₂.map f = f.asBoolAlg

full_name: BoolRing.hasForgetToBoolAlg_forget₂_obj
code: @[simps]
instance BoolRing.hasForgetToBoolAlg : HasForget₂ BoolRing BoolAlg 
goal: CategoryTheory.HasForget₂.forget₂.obj X = BoolAlg.of (AsBoolAlg ↑X)

full_name: instBooleanAlgebraαLatticeToLatToBddLatToBddDistLat
code: instance {X : BoolAlg} :
    BooleanAlgebra ↑(BddDistLat.toBddLat (X.toBddDistLat)).toLat 
goal: BooleanAlgebra ↑X.toBddDistLat.toBddLat.toLat

full_name: BoolAlg.hasForgetToBoolRing
code: @[simps]
instance BoolAlg.hasForgetToBoolRing : HasForget₂ BoolAlg BoolRing 
goal: CategoryTheory.HasForget₂ BoolAlg BoolRing

full_name: BoolAlg.hasForgetToBoolRing_forget₂_obj
code: @[simps]
instance BoolAlg.hasForgetToBoolRing : HasForget₂ BoolAlg BoolRing 
goal: CategoryTheory.HasForget₂.forget₂.obj X = BoolRing.of (AsBoolRing ↑X)

full_name: BoolAlg.hasForgetToBoolRing_forget₂_map
code: @[simps]
instance BoolAlg.hasForgetToBoolRing : HasForget₂ BoolAlg BoolRing 
goal: CategoryTheory.HasForget₂.forget₂.map f = f.asBoolRing

full_name: boolRingCatEquivBoolAlg
code: /-- The equivalence between Boolean rings and Boolean algebras. This is actually an isomorphism. -/
@[simps functor inverse]
def boolRingCatEquivBoolAlg : BoolRing ≌ BoolAlg 
goal: BoolRing ≌ BoolAlg

full_name: boolRingCatEquivBoolAlg_inverse
code: /-- The equivalence between Boolean rings and Boolean algebras. This is actually an isomorphism. -/
@[simps functor inverse]
def boolRingCatEquivBoolAlg : BoolRing ≌ BoolAlg 
goal: boolRingCatEquivBoolAlg.inverse = CategoryTheory.forget₂ BoolAlg BoolRing

full_name: boolRingCatEquivBoolAlg_functor
code: /-- The equivalence between Boolean rings and Boolean algebras. This is actually an isomorphism. -/
@[simps functor inverse]
def boolRingCatEquivBoolAlg : BoolRing ≌ BoolAlg 
goal: boolRingCatEquivBoolAlg.functor = CategoryTheory.forget₂ BoolRing BoolAlg