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_ult_const_2 : forall (A : Set) (x y : Map A) (z : prechain A), non_dist_chain A (concat A z x) -> iteres_ult_const_def_0 A (concat A z x) -> iteres_ult_const_def_0 A (concat A (concat A z x) y).