unfold Rminus in |- *; apply Rplus_le_compat_l.
unfold tstep in |- *; rewrite <- Ropp_0; left; apply Ropp_lt_gt_contravar;
apply Rinv_0_lt_compat; prove_sup.
Qed.

(**********)
Lemma MinDistance_lb_0 : (MinDistance_lb <= MinDistance)%R.
Proof with trivial.