proposition: Lemma mcoeff_poly_mul_rev p q m k : !|m| < k -> (p *M q)@_m = \sum_(k : 'X_{1..n < k, k} | m == (k.1 + k.2)%MM) p@_k.2 * q@_k.1.
proof: Proof. move=> /mcoeff_poly_mul ->; rewrite big_cond_mulrn. rewrite big_pairA /= exchange_big pair_bigA /=. by rewrite /= -big_cond_mulrn; apply/eq_big=> // i /=; rewrite addmC. 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