proposition: Lemma real_maxrN x : x \is real -> max x (- x) = `|x|.
proof: Proof. move=> x_real; rewrite /max. by case: real_ge0P => // [/ge0_cp [] | /lt0_cp []]; case: (@real_leP (- x) x); rewrite ?realN. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)