intros a; elim a; simpl in |- *; auto.
intros b H1; inversion H1.
intros n H b; case b; simpl in |- *; auto.
intros n0 H0; apply H.
apply lt_S_n; auto.
Qed.

Theorem le_bool_correct3 : forall a b : nat, le_bool a b = true -> a <= b.
Proof using.