proposition: Lemma map_mpolyE p k : msize p <= k -> p^f = \sum_(m : 'X_{1..n < k}) (f p@_m) *: 'X_[m].
proof: Proof. rewrite /map_mpoly; move/mmapE=> -> /=; apply/eq_bigr. by move=> i _; rewrite mmap1_id 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