proposition: Lemma BR_middle_prop1 a b: realp a -> realp b -> b -r (BRmiddle a b) = BRhalf (b -r a).
proof: Proof. move => ar br; rewrite /BRmiddle -{1} (BRhalf_double br) /BRhalf. rewrite - (BRprodBl RSh2 (RSp br RS2) (RSs ar br)) - (BRdouble_s br). by rewrite BRdiff_sum_simpl_r. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)