proposition: Lemma Rbar_lt_dec (x y : Rbar) : {Rbar_lt x y} + {~Rbar_lt x y}.
proof: Proof. destruct (Rbar_total_order x y) as [H|H] ; [ destruct H as [H|H]|]. now left. right ; rewrite H ; clear H ; destruct y ; auto ; apply Rlt_irrefl ; auto. right ; revert H ; destruct x as [x | | ] ; destruct y as [y | | ] ; intros H ; auto ; apply Rle_not_lt, Rlt_le ; auto. Qed.
imports: Coq(Reals ssreflect) Rcomplements