proposition: Lemma fgposP D : reflect (forall z, 0 <= coeff z D) (0 <=g D).
proof: Proof. apply: (iffP idP). + by move=> posD z; move/fgleP/(_ z): posD; rewrite coeff0. + by move=> posD; apply/fgleP=> 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)