trivial.
intros n ih.
rewrite ih.
trivial.
Qed.

(* Specifications: *)
Lemma max_Sn_n : forall n : nat, max (S n) n = S n.
simple induction n; clear n; simpl in |- *.
Lemma max_n_Sn : forall n : nat, max n (S n) = S n.
simple induction n; clear n; simpl in |- *.
Lemma max_n_O : forall n : nat, max n 0 = n.
intros n; elim n; clear n.