proposition: Lemma nonempty_Rdown E : Real.nonempty (Real.down E) <-> Real.nonempty E.
proof: Proof. by split=> [[_ [x Ex _]] | [x Ex]]; do 2?exists x. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)