proposition: Lemma fgscaleE c g k : (c *:g g)@_k = c * g@_k.
proof: Proof. rewrite {2}[g]monalgE !raddf_sum mulr_sumr. by apply/eq_bigr=> /= i _; rewrite !mcoeffU mulrnAr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path choice finset fintype finfun) mathcomp(tuple bigop ssralg ssrint ssrnum) xfinmap