Module M.
Function test_m (n:nat) : nat :=
match n with
| 0 => 0
| S n =>  S (S (test_m n))
end.
End M.
(* We redefine a new Function with the same name *)
Function test_m (n:nat) : nat :=
pred n.

Lemma test_m_is_pred : forall n, test_m n = pred n.