English
A simple order with decidable equality yields a linear order; i.e., any two elements are comparable.
Русский
Простой порядок с разрешимым равенством даёт линейный порядок; любые два элемента сравнимы.
LaTeX
$$$\text{IsSimpleOrder.linearOrder} : LinearOrder α$$$
Lean4
/-- A simple partial ordered `BoundedOrder` induces a lattice.
This is not an instance to prevent loops -/
protected def lattice {α} [DecidableEq α] [PartialOrder α] [BoundedOrder α] [IsSimpleOrder α] : Lattice α :=
@LinearOrder.toLattice α IsSimpleOrder.linearOrder