proposition: Lemma real_ge0P x : x \is real -> ger0_xor_lt0 x (min 0 x) (min x 0) (max 0 x) (max x 0) `|x| (x < 0) (0 <= x).
proof: Proof. move=> hx; rewrite -[X in `|X|]subr0; case: real_leP; by rewrite ?subr0 ?sub0r //; constructor. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)