proposition: Lemma BQ_middle_prop1 a b: ratp a -> ratp b -> b -q (BQmiddle a b) = BQhalf (b -q a).
proof: Proof. move => aq bq; rewrite /BQmiddle -{1} (BQhalf_double bq) /BQhalf. rewrite - (BQprodBl QSh2 (QSdouble bq) (QSs aq bq)). by rewrite -/(BQdouble b) - (BQdouble_p bq) BQdiff_sum_simpl_r. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)