proposition: Lemma BQnum0_P q : ratp q -> Qnum q = \0z -> q = \0q.
proof: Proof. move => qq n0. move/BQ_P: (qq) => [_ nz dp cp]. rewrite - (BQ_pr2 qq) /BQ_zero (BQ_of_Z_pr0 ZS0). apply/ (BQ_of_pair_prop5 nz dp ZS0 ZpsS1). by rewrite n0 BZprod_0l BZprod_0r. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)