# proof that $C_\cup$ and $C_\cap$ are consequence operators

## Primary tabs

Type of Math Object:
Proof
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### preamble problem

When I last had a look at the entry two weeks ago, it was fine.
Now, when I revisited it, it was broken. The computer had thrown
away the preamble and replaced it with the default preamble (in
which "theorem", "definition", and "proof" are undefined (although
they really should be)). Has anyone else had this experience?
This, alomg with the problem of the entry which was shown to be
an attachement when it was not, suggests that there might be some
instability in the database.

### Re: preamble problem

I've never had this problem. I suspect it's rather rare: I've just Googled for broken entries on PlanetMath, and yours (now fixed) is the only one that comes up.

I think the attachment problem was caused by the parent being deleted. (If there were a log of deletions, as has been suggested before, this would be easy to check.) The fact that the "Attached to" box appears empty doesn't surprise me, as I've noticed before that this information doesn't appear to be stored as text (since the canonical names I enter are often changed to non-canonical names when I next edit the entry) - the box may be empty not because there is no parent specified, but because the system cannot find a name for the specified parent (because it's been deleted).