proposition: Lemma msymMK (p q : {mpoly R[n]}) : p != 0 -> p \is symmetric -> p * q \is symmetric -> q \is symmetric.
proof: Proof. move=> nz_p /issymP sym_p /issymP sym_pq; apply/issymP => s. by move/(_ s): sym_pq; rewrite msymM sym_p => /(mulfI nz_p). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg