I don't think you really could rewrite the rules any better. There about the most hole-free, abuseless rules GW has ever come up with.

the sentinels who paced the ramparts

My appointment book is pretty full, but I can just squeeze you in.

To clarify these ideas for the reader, let us show, without the axiom of choice, that a product of finitely many nonempty sets is nonempty: This is done by induction on the number n of sets. […] The finite axiom of choice is not an axiom, but rather a theorem that can be proved from the other axioms. In contrast, there are weak forms of the axiom of choice that are not provable.