intros x y H' H'0; case (Zle_lt_or_eq _ _ H').
intros H'1; rewrite Zmult_comm; apply Zmult_gt_0_le_0_compat; auto;
apply Zlt_gt; auto.
intros H'1; rewrite <- H'1; simpl in |- *; auto with zarith.
Qed.
Hint Resolve Zle_mult_gen: zarith.
Definition Zmax : forall x_ x_ : Z, Z :=
fun n m : Z =>
match (n ?= m)%Z with
| Datatypes.Eq => m
| Datatypes.Lt => m
| Datatypes.Gt => n
end.

Theorem ZmaxLe1 : forall z1 z2 : Z, (z1 <= Zmax z1 z2)%Z.
intros z1 z2; unfold Zmax in |- *; CaseEq (z1 ?= z2)%Z; simpl in |- *;
auto with zarith.