proposition: Lemma BQ_middle_prop2 a b: ratp a -> ratp b -> (BQmiddle a b) -q a = BQhalf (b -q a).
proof: Proof. move => aq bq. rewrite /BQmiddle -{2} (BQhalf_double aq) /BQhalf. rewrite - (BQprodBl QSh2 (QSs aq bq)(QSdouble aq)). by rewrite -/(BQdouble _) - (BQdouble_p aq) BQdiff_sum_simpl_l. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)