proposition: Lemma BQ_of_Z_iQm z: inc z BZm -> inc (BQ_of_Z z) BQm.
proof: Proof. case: (equal_or_not z \0z) => z0 zm. rewrite z0. apply:Zo_i; [ apply: BQ_of_Z_iQ; apply:ZS0 | rewrite/BQ_of_Z;aw; apply: ZmS0]. by apply:(BQms_sBQm); apply: BQ_of_Z_iQms; apply/BZms_iP. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)