proposition: Lemma dvdz_contents a p : (a %| zcontents p)%Z = (p \is a polyOver (dvdz a)).
proof: Proof. rewrite dvdzE abszM absz_sg lead_coef_eq0. have [-> | nz_p] := eqVneq; first by rewrite mul0n dvdn0 rpred0. rewrite mul1n; apply/dvdn_biggcdP/(all_nthP 0)=> a_dv_p i ltip /=. exact: (a_dv_p (Ordinal ltip)). exact: a_dv_p. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly ssrnum ssrint archimedean rat matrix) mathcomp(polydiv perm zmodp mxalgebra vector)