(** 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] *)

Axiom ex_min_P : forall P, (forall x, {P x}+{~(P x)}) -> ex P -> ex (min P).