proposition: Lemma freeg_mulz k (m : int) (S : K) : << k *g S >> *~ m = << k *~ m *g S >>.
proof: Proof. case: m=> [n|n]. + by rewrite -pmulrn freeg_muln. + by rewrite NegzE -nmulrn freeg_muln mulrNz freegUN. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)