proposition: Lemma ltR_neqAle x y : x < y <-> x != y /\ x <= y.
proof: Proof. by rewrite (leR_eqVlt x y); split=> [ltxy|[neqxy []]//]; split; [case | right]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div order) mathcomp(ssralg ssrnum ssrint rat intdiv) Coq(Morphisms Setoid) fourcolor(real realsyntax)