proposition: Lemma Nreal_gtF x y : y \is real -> x \notin real -> (y < x) = false.
proof: Proof. by move=> yR xNR; rewrite lt_def Nreal_geF ?andbF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)