mk — Mathlib · SciLib

English

Construct an isomorphism of complete lattices from an order isomorphism between them.

Русский

Построить изоморфизм полных решёток из ордер-изоморфизма между ними.

LaTeX

$$$$ \exists I: \alpha \cong \beta. $$$$

Lean4

/-- Constructs an isomorphism of complete lattices from an order isomorphism between them. -/
@[simps]
def mk {α β : CompleteLat.{u}} (e : α ≃o β) : α ≅ β
    where
  hom := ConcreteCategory.ofHom e
  inv := ConcreteCategory.ofHom e.symm
  hom_inv_id := by ext; exact e.symm_apply_apply _
  inv_hom_id := by ext; exact e.apply_symm_apply _

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