apply Rlt_trans with (V + ConflictRange)%R...
unfold V, ConflictRange in |- *; simpl in |- *; prove_sup...
apply MinDistance_lb_majoration...
Qed.

(* Specifications: *)
(**********)
Lemma MinDistance_pos : (0 < MinDistance)%R.
apply Rlt_le_trans with MinDistance_lb.