English
From an order isomorphism e : α ≃o β, there is a HeytAlg isomorphism α ≅ β with hom := ofHom e and inv := ofHom e.symm, and the usual inverses.
Русский
Из Ordnung-изоморфизма e : α ≃o β строится изоморфизм HeytAlg α ≅ β с hom := ofHom e и inv := ofHom e.symm, а также обратные соотношения.
LaTeX
$$$ \exists \phi : \alpha \cong \beta, \phi.\mathrm{hom} = \mathrm{ofHom}(e) \land \phi.\mathrm{inv} = \mathrm{ofHom}(e^{-1}) $$$
Lean4
/-- Constructs an isomorphism of Heyting algebras from an order isomorphism between them. -/
@[simps]
def mk {α β : HeytAlg.{u}} (e : α ≃o β) : α ≅ β where
hom := ofHom e
inv := ofHom e.symm
hom_inv_id := by ext; exact e.symm_apply_apply _
inv_hom_id := by ext; exact e.apply_symm_apply _
