proposition: Lemma real_leP x y : x \is real -> y \is real -> ler_xor_gt x y (min y x) (min x y) (max y x) (max x y) `|x - y| `|y - x| (x <= y) (y < x).
proof: Proof. move=> xR yR; case: (comparable_leP (real_leVge xR yR)) => xy. - by rewrite [`|x - y|]distrC !ger0_norm ?subr_cp0 //; constructor. - by rewrite [`|y - x|]distrC !gtr0_norm ?subr_cp0 //; 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)