proposition: Lemma sgz_lead_primitive p : sgz (lead_coef (zprimitive p)) = (p != 0).
proof: Proof. have [-> | nz_p] := eqVneq; first by rewrite zprimitive0 lead_coef0. apply: (@mulfI _ (sgz (zcontents p))); first by rewrite sgz_eq0 zcontents_eq0. by rewrite -sgzM mulr1 -lead_coefZ -zpolyEprim sgz_contents. 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)