proposition: Lemma freegUD k1 k2 x : << k1 *g x >> + << k2 *g x >> = << (k1 + k2) *g x >>.
proof: Proof. by apply/eqP/freeg_eqP=> z; rewrite coeffD !coeffU -mulrDl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)