proposition: Lemma qlt_cN a b: natp a -> natp b -> (a <c b <-> BQ_of_nat a <q BQ_of_nat b).
proof: Proof. move => aN bN. by apply: (iff_trans (zlt_cN aN bN)); apply:qlt_cZ; apply:BZ_of_nat_i. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)