proposition: Fact lt_def x y : (x < y) = (y != x) && (x <= y).
proof: Proof. rewrite le_def; case: eqVneq => //= ->; rewrite -sub_gt0 subrr. by apply/idP=> lt00; case/negP: (lt0_ngt0 lt00). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)