proposition: Lemma BZopp_sign x: intp x -> BZsign (BZopp x) = BZopp (BZsign x).
proof: Proof. move => xz. case/BZ_i1P:(xz) => xs. + by rewrite xs BZopp_0 BZsign_0 BZopp_0. + by rewrite (BZsign_pos xs) BZopp_1 BZsign_neg //; apply:BZopp_positive1. + by rewrite (BZsign_neg xs) BZopp_m1 BZsign_pos //;apply:BZopp_negative1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)