proposition: Lemma pp_mull : forall a p, a != 0 -> pp (a%:P * p) %= pp p.
proof: Proof. move=> a p a0. apply: (eqd_trans (pp_mul a%:P p)). by rewrite -{2}[pp p]mul1r eqd_mul ?ppC ?(eqP a0). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(path choice fintype tuple finset ssralg) mathcomp(matrix poly) mathcomp(bigop polydiv) CoqEAL(stronglydiscrete dvdring)