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).
Hint Resolve rel_iter_bound_iter rel_iter_iter_bound : core.
(* A characterization of fun n x y => rel_iter R n x y with a diophantine formula (to be proved in dio_expo.v) when the relation R does not grow more that linearly *)

Theorem rel_iter_bound_equiv n x y : rel_iter R n x y <-> rel_iter_bound n x y.