intros a; elim a; simpl in |- *; auto.
intros b; case b; simpl in |- *; auto with arith.
intros n H b; case b; simpl in |- *; try (intros; discriminate);
auto with arith.
Qed.

(* Specifications: *)
Theorem le_bool_correct4 : forall a b : nat, le_bool a b = false -> b <= a.
Proof using.