proposition: Lemma mpolyX_prod s P : \prod_(i <- s | P i) 'X_[i] = 'X_[\sum_(i <- s | P i) i].
proof: Proof. elim: s => [|i s ih]; first by rewrite !big_nil mpolyX0. by rewrite !big_cons; case: (P i); rewrite ?mpolyXD ih. 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