Definition iteres_ult_const_def_0 (A : Set) (p : prechain A) : Prop :=
forall (f : Map A -> Map A) (x : Map A) (n : nat),
p = iteres A f x n ->
non_dist_chain A p ->
exists q : nat, S q <= n /\ power (Map A) f x q = power (Map A) f x (S q).

Lemma iteres_dom_ok :
forall (A : Set) (T : mEnsemble A) (f : Map A -> Map A)
(x : Map A) (n : nat),
T x -> def_ok_app A T f -> prechain_dom_ok A T (iteres A f x n).