Section rel_iter_bound.
Variable (R : nat -> nat -> Prop) (k : nat) (Hk1 : forall x y, R x y -> y <= k*x).
Let Hk' : forall x y, R x y -> y <= (S k)*x.
Notation power := (mscal mult 1).
Notation "∑" := (msum plus 0).

Lemma rel_iter_iter_bound n x y : rel_iter R n x y -> rel_iter_bound n x y.