proposition: Lemma mpolyOver_mpoly (S : {pred R}) E : (forall m : 'X_{1..n}, m \in dom E -> coeff m E \in S) -> [mpoly E] \is a mpolyOver S.
proof: Proof. move=> S_E; apply/(all_nthP 0)=> i; rewrite size_map /= => lt. by rewrite (nth_map 0%MM) // mcoeff_MPoly S_E ?mem_nth. 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