proposition: Lemma BQprod_0r x: ratp x -> x *q \0q = \0q.
proof: Proof. move /BQ_P => [_ _ pa _]; move:(BZps_sBZ pa) => pb. rewrite /BQprod /BQ_zero /BQ_of_Z pr1_pair pr2_pair BZprod_0r. by rewrite BZprod_1r //; apply: BQnum0_P1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)