proposition: Lemma mderivnE i k p : p^`M(i, k) = \sum_(m <- msupp p) (((m i)^_k)%:R * p@_m) *: 'X_[m - U_(i) *+ k].
proof: Proof. rewrite mderivmE; apply/eq_bigr=> /= m _. rewrite -commr_nat (bigD1 i) //= big1 ?muln1. by rewrite mulmnE mnm1E eqxx mul1n. by move=> j ne_ji; rewrite mulmnE mnm1E eq_sym (negbTE ne_ji). 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