proposition: Lemma rgt_diffP a b: realp a -> realp b -> (a -r b <r \0r <-> a <r b).
proof: Proof. move => ar br; rewrite - (BRoppB br ar). apply:iff_sym;apply: (iff_trans(rlt_diffP ar br)); split. by move => /BRopp_positive1 / rgt0xP. by move/ rgt0xP => /BRopp_negative1; rewrite BRopp_K//; apply:RS_diff. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)