proposition: Lemma mesym_neq0 k (le_kn : k <= n) : 's_k != 0 :> {mpoly R[n]}.
proof: Proof. apply/eqP=> z_sk; pose h : {set 'I_n} := mesymlmnm k. have := mem_mesym1_mesym h; rewrite card_mesymlmnm //. by rewrite mcoeff_msupp z_sk mcoeff0 eqxx. 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