proposition: Lemma dom_eq0 (D : {freeg K / R}) : (dom D == [::]) = (D == 0).
proof: Proof. apply/eqP/idP => [z_domD|/eqP ->]; last exact: dom0. by apply/freeg_eqP => z; rewrite coeff0 coeff_outdom // z_domD in_nil. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)