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