proposition: Lemma sup_le_ub y : ub E y -> sup E <= y.
proof: Proof. by move=> ubEy a /open[b]; left; split; last by exists b => // z ?; apply: ubEy. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq order) mathcomp(ssralg ssrnum ssrint rat) fourcolor(real) Coq(Setoid Morphisms)