proposition: Lemma pp_eq0 : forall p, (pp p == 0) = (p == 0).
proof: Proof. move=> p. rewrite {2}(ppP p) mulf_eq0. apply/idP/idP; first by move->; rewrite orbT. case/orP=> //. by rewrite polyC_eq0 gcdsr_eq0 => /eqP->; rewrite pp0. 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)