proposition: Lemma fgneg_eq0P (D : {freeg K}) : D <=g 0 -> deg D = 0 -> D = 0.
proof: Proof. move=> negD deg_eq0; apply/eqP; rewrite -oppr_eq0; apply/eqP. apply/fgpos_eq0P; last by apply/eqP; rewrite degN oppr_eq0 deg_eq0. apply/fgposP=> z; rewrite coeffN oppr_ge0. by move/fgleP: negD => /(_ z); rewrite coeff0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order generic_quotient) mathcomp(ssralg ssrnum ssrint)