When you have a tree, you have a choice of which order to apply the rules to the tree. We want to

show that this choice does not affect the result of your proof. Using the Soundness and Completeness

Lemmas, show that, if a tree closes when rules are applied in one order, it also closes when rules are

applied in a different order.

TIP: Assume a given tree closes when the rules are applied in one order, and remains open when they

are applied in a different order. Then use the Soundness and Completeness Lemmas to derive a

contradiction.