proposition: Lemma mdegM : {morph mdeg: m1 m2 / (m1 * m2)%M >-> (m1 + m2)%N }.
proof: Proof. move=> m1 m2 /=; rewrite mdegE mdomD. rewrite (mdegEw (fsubsetUl _ (finsupp m2))) (mdegEw (fsubsetUr (finsupp m1) _)). by rewrite -big_split /=; apply/eq_bigr=> /= i _; rewrite cmM. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path choice finset fintype finfun) mathcomp(tuple bigop ssralg ssrint ssrnum) xfinmap