proposition: Lemma ord_sup_sub X: ordinal_set X -> ~ (inc (\osup X) X) -> forall x, inc x X -> x <o (\osup X).
proof: Proof. by move=> h1 h2 x xX; split; [apply: ord_sup_ub | dneg xs; rewrite -xs ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)