Sort of a legal question, so your humble opinion is sought:.
I’m looking at a patent which seems, on consideration, to be just worthless. All the claims are anticipated by prior art. But… all the prior art is contingent on narrower claims. Like
New Patent: “Everything that is red”
Old patent claim 1 “Anti-Gravity machine”
Old patent claim 2 “Claim 1, and painted red”
Is new patent inovative? Does old patent claim 2 invalidate new patent? Does it partially invalidate it?
I’m unclear about the question. Are you applying for a patent and think that an existing patent was issued in error? Are you seeking damages because a patent you own has been violated?
The Patent Office website has pretty good information about several situations and there are many other resources available. But this sounds like you are thinking of taking some sort of legal action.
Whole books can (and have) been written on it, but a patent has to be something that is patentable, non-obvious and not be prior art (and useful, which is US only). SO ends theory.
The US Court of Appeals for the Federal Circuit has, since the 1980’s greatly, ridiculously expanded the scope of what is patentable and what is non-obvious and what is not prior art (note business method patents). Since the US is (for now) the world’s largest economy, this has many ramifications for everyone, nobody thought “business methods” were patentable (the occassional order here and there notwithstanding).
This is esoteric stuff where the devil is in the details so it is usually very hard to say things like ‘all the claims are anticipated by prior art’ without extended analysis. Allowed patent claims also have a presumption of validity in court since they have been through the examination process.
However, in general, narrower claims in valid prior art that disclose every element of the claim in question are considered a disclosure. And it doesn’t have to be in the claims, it can be anywhere in the prior art specification.
In your example, the allowed claim is very broad of course and any specific example of something that is red in the prior art could be an invalidating disclosure.
I am not your lawyer.
What Folly said. You’re sure it’s an issued patent and not a patent application publication? The two can look very similar.
I don’t know what country you are looking at, but in the U.S. if it’s a fairly recent patent you can typically look up the prosecution history and see what went down. It can be instructive.
Yes, and I simplified the example 
(There didn’t seem to be much point giving details of something that can only really be determined by detailed examination. The patent is an Australian Inovation Patent, [2013100349] which means it is granted without full examination. At first glance Claim 1 appears to be valid, because there are no other patents which have that as the primary claim, and it is a new technology. But on further examination, it appears that the idea was so obvious it was only ever claimed as an additional claim)
Oh, an innovation patent. Yeah, those are indeed basically worthless until they are examined because they are not enforceable until then.
Ok, so taking your example, and cleaning it up a bit.
NC 1: “An object that is red.”
OC 1 “Anti-Gravity machine”
OC 2 “OC 1 that is red”
As a simple analysis, NC1 claims all red objects. If there is prior art (basically, a publicly available red object) before the priority date, then NC1 is invalid. OC2 appears to demonstrate a red object, and so OC2 is prior art for NC1.
If we were in a real court action, it might be possible for a court to allow an amendment of NC1 to exclude prior art (“An object which is not a anti-gravity machine that is red”) and I guess you could call that partial invalidation, but usually we would say a patent is partially invalidated if certain of its claims were invalidated but certain claims left standing. So NC1 might be invalid but NC2 might stand
That said, NC1 could have dependent claims that are narrower, so even if NC1 is invalid NC2 might be valid.
You also have to be careful here. There does not have to be a prior claim to the subject matter for the prior art to invalidate the claim in question. Merely being described (and not just in a patent, in almost any publicly available document) is sufficient to invalidate a patent claim.
For such a simply formatted claim, they typically tend to stand or fall completely. Finding one prior art reference that falls within the scope of the claim is sufficient to invalidate the entire scope of the claim. This is why examination is important: you try to find all these problems prior to issue, when the scope of the claim can still be amended.
There are more complicated types of claims which can be partially invalidated, but getting into those details is probably too complicated for this thread.