by rewrite gcd0p size_polyC oner_eq0.
rewrite ltnS leqn0 size_poly_eq0; move/eqP->; rewrite gcdp0 modp0 size_polyC.
by rewrite oner_eq0.
Qed.

Lemma eqp_gcdl r p q :  p %= q -> gcdp p r %= gcdp q r.
move=> eqr; rewrite /eqp !(dvdp_gcd, dvdp_gcdr, andbT) /=.