proposition: Lemma qle_cN a b: natp a -> natp b -> (a <=c b <-> BQ_of_nat a <=q BQ_of_nat b).
proof: Proof. move => az bz. by apply: (iff_trans (zle_cN az bz)); apply:qle_cZ; apply:BZ_of_nat_i. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)