proposition: Lemma lt0_cp x : x < 0 -> (x <= 0) * (0 <= - x) * (x <= - x) * (0 < - x) * (x < - x).
proof: Proof. move=> hx; move: (ltW hx) => hx'; rewrite !le0_cp // hx'. by rewrite oppr_cp0 hx // (@lt_trans _ _ 0) ?oppr_cp0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)