proposition: Lemma BQ_of_pair_opp a b: intp a -> inc b BZps -> (BQ_of_pair (BZopp a) b) = BQopp (BQ_of_pair a b).
proof: Proof. move => az bzps; move:(BZps_sBZ bzps) => bz. rewrite /BQ_of_pair -lock /BQ_of_pair_internal /BQopp -(BZgcd_opp az bz); aw. by rewrite (BZquo_opp2 (BZgcd_div2 az bz)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)