∀ {α : Type u_2} {β : Type u_1} [inst : Max α] [inst_1 : Min α] [inst_2 : LE α] [inst_3 : LT α] [inst_4 : Top α]
  [inst_5 : Bot α] [inst_6 : HNot α] [inst_7 : SDiff α] [inst_8 : CoheytingAlgebra β] (f : α → β)
  (hf : Function.Injective f) (le : ∀ {x y : α}, f x ≤ f y ↔ x ≤ y) (lt : ∀ {x y : α}, f x < f y ↔ x < y)
  (map_sup : ∀ (a b : α), f (a ⊔ b) = f a ⊔ f b) (map_inf : ∀ (a b : α), f (a ⊓ b) = f a ⊓ f b),
  f ⊤ = ⊤ →
    ∀ (map_bot : f ⊥ = ⊥),
      (∀ (a : α), f (￢a) = ￢f a) → ∀ (map_sdiff : ∀ (a b : α), f (a \ b) = f a \ f b) (a : α), f (⊤ \ a) = f (￢a)