proposition: Lemma leR_lt_trans x y z : x <= y -> y < z -> x < z.
proof: Proof. by move=> lexy ltyz lezx; have:= leR_trans lezx lexy. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)