proposition: Lemma msymZ c p s : msym s (c *: p) = c *: (msym s p).
proof: Proof. pose_big_enough i; first rewrite !(msymE s i) //. rewrite scaler_sumr; apply/eq_bigr => j _. by rewrite mcoeffZ scalerA. by close. 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