proposition: Lemma gtr0_sg x : 0 < x -> sg x = 1.
proof: Proof. by move=> x_gt0; rewrite /sg gt_eqF // lt_gtF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)