I'm typesetting a math paper, where at many points I need to break proofs into several cases. I've been putting these just in an itemize environment, but this is a confusing, because things like "Case 1" are no longer uniquely-defined; I want the names to have global scope, so I can refer back to sub-cases of previous theorems.
Ideally, I'd like something like itemize, but with a separate counter indicating how many times the environment has been used. Then the cases should show as something like (A1) (A2) (A3) in the first appearance of the environment, (B1) (B2) (B3) in the second, etc.
Is there a package or other easy way to handle this?