proposition: Lemma sup_sup E : Real.has_sup E -> forall x, Real.ub E x <-> sup E <= x.
proof: Proof. by case=> hasE ubE x; split; [apply: sup_le_ub | apply: ge_sup_ub]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)