As for the first sentence, it seems yes. Since the word "books" is followed by a relative clause then this makes it definite.
(Correction: Sorry for the confusion, please see post 4 below http://www.usingenglish.com/forum/256369-post4.html )
The second one however has two possibilities but with two different meanings:
If you say "the claim", it is OK. The meaning here, or actually the emphasis, is on one defnite claim that John has made. If you say "the claim", I will uunderstand that he has made one claime and this one claim was made against Mary.
If you say however "a claim", then it means that you are referring to "one of the claims" made by John. The article "a" is used sometimes to mean "one of...." Example: He is a son of Sarah. (As if you are saying that Sarah has other children)
Again for sentence No 2, I feel that what determines whether "a" or "the" should be used is not in fact what comes after the claim. Rather, it is determined on what has come before the whole sentence.
My feeling is that should sentence No 2 be preceeded by no other sentence, then it should have "a claim" rather than "the claim". As a matter of fact, "the" is usually used whenever the broader context shows that the conversation participants have already known that there is a claim before using sentence No 2.