English
From an order isomorphism e: α ≃o β there is an isomorphism α ≅ β in SemilatInfCat with the appropriate hom and inv.
Русский
Из порядочного изоморфизма e: α ≃o β получается изоморфизм α ≅ β в SemilatInfCat с соответствующими гом и инв.
LaTeX
$$$ \\alpha \\cong \\beta \\text{ from } e: \\alpha \\equiv_o \\beta $ with \\mathrm{hom} = e, \\mathrm{inv} = e^{-1} $$$
Lean4
/-- Constructs an isomorphism of lattices from an order isomorphism between them. -/
@[simps]
def mk {α β : SemilatSupCat.{u}} (e : α ≃o β) : α ≅ β
where
hom := (e : SupBotHom _ _)
inv := (e.symm : SupBotHom _ _)
hom_inv_id := by ext; exact e.symm_apply_apply _
inv_hom_id := by ext; exact e.apply_symm_apply _
