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 dvdp_gcd_idl m n : m %| n -> gcdp m n %= m.