proposition: Lemma Rltb_def x y : (Rltb x y) = (y != x) && (Rleb x y).
proof: Proof. apply/(sameP (RltbP x y))/(iffP idP). case/andP=> /eqP H /RlebP/Rle_not_gt H2. by case: (Rtotal_order x y)=> // [][] // /esym. move=> H; apply/andP; split; [apply/eqP|apply/RlebP]. exact: Rgt_not_eq. exact: Rlt_le. Qed.
imports: Rdefinitions Raxioms RIneq Rbasic_fun Zwf Epsilon FunctionalExtensionality Ranalysis1 Rsqrt_def Rtrigo1 Reals mathcomp(all_ssreflect ssralg poly mxpoly ssrnum) HB(structures)