(** The distance between [x (2m)] and [x m] defined using [epsilon] *)
Definition min P i := P i /\ forall j, P j -> i <= j.
Definition dist_x2m_xm m := epsilon (min (sep_x2m_xm m)).
(** Existence of this distance whenever [lambda <= m] *)

Lemma ex_dist_x2m_xm : forall m, lambda <= m -> ex (min (sep_x2m_xm m)).
Definition variant m := (lambda - m, dist_x2m_xm m).