Example

To show D |^_ H need to consider the sentence corresponding to instruction b.

From this derive:

        [e º x' Ù Q₁ee Ù S₀ee] ® [Q₂e'x Ù (S₀ex ® S₀e'x)]

From d₀ with n = 0 we get

        Q₁ee Ù S₀ee Ù [e º x' ® S₀ex]

So

         e º x' ® Q₂e'x Ù S₀e'x

By [Succ]

        $tx(Q₂e'x Ù S₀e'x)

And H follows by Existential Generalization.