(* THERE EXISTS j <= n S.T. zj = t: COMMON DEF. EQUIVALENT TO INDUCTIVE DEF.: *)

(* Specifications: *)
Lemma ex_j_exist_j:forall(m:fmap)(z t:dart)(n:nat),
ex_j m z t n <->
exists j :nat, (j <= n)%nat /\ Iter (f m) j z = t.