English
From an order isomorphism e: α.carrier ≃o β.carrier, there is an isomorphism α ≅ β in FinBddDistLat with hom := ofHom e and inv := ofHom e.symm, satisfying the usual inverse laws.
Русский
Из ордерного изоморфизма e между карриерами α и β существует изоморфизм α ≅ β в FinBddDistLat с гомоморфизмом hom := ofHom e и обратным inv := ofHom e.symm, удовлетворяющим обычным законам обратного.
LaTeX
$$$ \\exists \\mathcal{I} : \\alpha \\cong \\beta \\text{ with } \\mathcal{I}.hom = \\mathrm{ofHom}(e) \\text{ and } \\mathcal{I}.inv = \\mathrm{ofHom}(e^{-1}). $$$
Lean4
/-- Constructs an equivalence between finite distributive lattices from an order isomorphism
between them. -/
@[simps]
def mk {α β : FinBddDistLat.{u}} (e : α.carrier ≃o β.carrier) : 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 _
