proposition: Lemma real_sup_total E x : Real.has_sup E -> Real.down E x \/ Real.sup E <= x.
proof: Proof. exact: (Real.sup_total R). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)