proposition: Lemma sym_anti p q : p \is antisym -> q \is symmetric -> p * q \is antisym.
proof: Proof. Proof using. move=> /isantisymP Hsym /issymP Hanti. apply/isantisymP => s. rewrite msymM Hsym Hanti. by case: (odd_perm _); rewrite !simplexp. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg ssrint fingroup perm zmodp binomial) mathcomp(ssrcomplements freeg mpoly) tools permcomp presentSn sorted partition