proposition: Lemma real_ltgtP x y : x \is real -> y \is real -> comparer x y (min y x) (min x y) (max y x) (max x y) `|x - y| `|y - x| (y == x) (x == y) (x >= y) (x <= y) (x > y) (x < y).
proof: Proof. move=> xR yR; case: (comparable_ltgtP (real_leVge yR xR)) => [?|?|->]. - by rewrite [`|y - x|]distrC !gtr0_norm ?subr_gt0//; constructor. - by rewrite [`|x - y|]distrC !gtr0_norm ?subr_gt0//; constructor. - by rewrite subrr normr0; 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)