proposition: Lemma BQprod_Mlt1 a b: ratp a -> inc b BQps -> (a /q b <q \1q <-> a<q b).
proof: Proof. move =>ap bp; move:(QpsS_inv bp) => cp. move/ BQps_iP: bp => [/BQp_sBQ bq bnz]. by move: (BQprod_plt2r ap bq cp); rewrite (BQprod_inv1 bq bnz). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)