proposition: Lemma BQps_iP x: inc x BQps <-> inc x BQp /\ x <> \0q.
proof: Proof. split; first by move => h; split; [ apply:BQps_sBQp | apply: BQps_nz]. move => [ /Zo_P [xq nxp] xnz ]; apply: Zo_i => //. by apply/BZps_iP; split => //; move/(BQnum0_P xq). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)