Definition t := O.t.Definition eq := O.eq.#[global]
Program Instance eq_equiv : Equivalence eq.Definition eq_dec := O.eq_dec.Definition lt := flip O.lt.Definition le := flip O.le.#[global]
Instance lt_strorder: StrictOrder lt.#[global]
Instance lt_compat : Proper (eq==>eq==>iff) lt.

Lemma le_lteq : forall x y, le x y <-> lt x y \/ eq x y.