proposition: Lemma ge_sup_ub E x : Real.has_ub E -> sup E <= x -> Real.ub E x.
proof: Proof. by move/sup_ub=> ubE leEx y /ubE-leyE; apply: leR_trans leEx. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)