proposition: Lemma has_ub_Rdown E : Real.has_ub (Real.down E) <-> Real.has_ub E.
proof: Proof. by rewrite /Real.has_ub; setoid_rewrite ub_Rdown. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)