proposition: Lemma comp_mpolywE p lq w : msize p <= w -> p \mPo lq = \sum_(m : 'X_{1..n < w}) (p@_m *: \prod_(i < n) (tnth lq i)^+(m i)).
proof: Proof. move=> le_szp_w; rewrite /comp_mpoly (mmapE w) //=. by apply/eq_bigr=> m _; rewrite mul_mpolyC. 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