proposition: Lemma osups_least X x: ordinalp x -> (forall y, inc y X -> y <o x) -> osups X <=o x.
proof: Proof. move => ox ha. rewrite /osups. Ytac h; first by apply/oleSltP; apply: ha. by apply:(ord_ub_sup ox) => y /ha []. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)