proposition: Lemma map_poly_divzK {a} p : p \is a polyOver (dvdz a) -> a *: map_poly (divz^~ a) p = p.
proof: Proof. move/polyOverP=> a_dv_p; apply/polyP=> i. by rewrite coefZ coef_map_id0 ?div0z // mulrC divzK. 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)