proposition: Lemma ltr0_sgz x : x < 0 -> sgz x = -1.
proof: Proof. by move=> x_lt0; rewrite /sgz eq_sym eq_le x_lt0 lt_geF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(fintype finfun bigop order ssralg countalg ssrnum) mathcomp(poly)