Instance CompSpecs : compspecs. make_compspecs prog. Defined.
Definition Vprog : varspecs. mk_varspecs prog. Defined.
Fixpoint fib_of_nat (n: nat): Z :=
match n with
| O => 0
| S n' =>
match n' with
| O => 1
| S n'' => fib_of_nat n'' + fib_of_nat n'
end
end.
Definition fib_of_Z (n: Z): Z := fib_of_nat (nat_of_Z n).

Lemma fib_ordered: forall n, 0 <= n -> fib_of_Z n <= fib_of_Z (n + 1).