proposition: Lemma BQsign_abs x: ratp x -> x *q (BQQsign x) = BQabs x.
proof: Proof. move => xq; case /BQ_i1P: (xq) => xs. + rewrite xs BQabs_0 BQprod_0l //; apply:QS_qsign. + by rewrite (BQabs_pos (BQps_sBQp xs)) /BQQsign (BQsign_pos xs) BQprod_1r. + by rewrite (BQabs_negs xs) /BQQsign (BQsign_neg xs) (BQprod_m1r xq). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)