proposition: Lemma gt0_cp x : 0 < x -> (0 <= x) * (- x <= 0) * (- x <= x) * (- x < 0) * (- x < x).
proof: Proof. move=> hx; move: (ltW hx) => hx'; rewrite !ge0_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)