proposition: Lemma gtr0_sgz x : 0 < x -> sgz x = 1.
proof: Proof. by move=> x_gt0; rewrite /sgz lt_neqAle andbC eq_le lt_geF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(fintype finfun bigop order ssralg countalg ssrnum) mathcomp(poly)