Can one say something like "This seems to be valid in the general case, but is not proven there"? Or must one say "then"?
There refers to a location. I believe in this case, the "location" would be within whatever "the general case" refers to. If you were to replace "there" with "in that general case", it should mean the same thing.
This seems to be valid in the general case, but is not proven in that general case.
Same meaning, yes? Because you can replace "there" with a location, it follows that "there" is the proper word to use.