proposition: Lemma real_ltgt0P x : x \is real -> comparer0 x (min 0 x) (min x 0) (max 0 x) (max x 0) `|x| (0 == x) (x == 0) (x <= 0) (0 <= x) (x < 0) (x > 0).
proof: Proof. move=> hx; rewrite -[X in `|X|]subr0; case: (@real_ltgtP 0 x); 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)