proposition: Lemma gcdp_scalel c m n : c != 0 -> gcdp (c *: m) n %= gcdp m n.
proof: Proof. move=> cn0; rewrite /eqp dvdp_gcd [gcdp m n %| _]dvdp_gcd !dvdp_gcdr !andbT. apply/andP; split; last first. by apply: dvdp_trans (dvdp_gcdl _ _) _; rewrite dvdpZr. by apply: dvdp_trans (dvdp_gcdl _ _) _; rewrite dvdpZl. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)