(* THERE EXISTS j <= n S.T. zj = t: INDUCTIVE DEF. *)
Fixpoint ex_j
(m:fmap)(z t:dart)(n:nat){struct n}:Prop:=
match n with
0%nat => z = t
| S n0 => Iter (f m) n z = t \/ ex_j m z t n0
end.

(* Specifications: *)
Lemma ex_j_dec:
forall(m:fmap)(z t:dart)(n:nat),
{ex_j m z t n} + {~ex_j m z t n}.