Problem in a nutshell: I'd like to number theorems that are embedded within other theorems' proofs with numbers that indicate the parent-child relationship between the two theorems.
Problem in detail: When embedding theorems etc. inside other theorems' proofs, the embedded items are numbered using the same counter as the parent theorem. For instance, if the parent theorem is "Theorem 3", a theorem embedded in Theorem 3's proof will be dubbed "Theorem 4". I'd like the embedded theorems etc. to be numbered hierarchically, so that, to continue the example, the embedded theorem will be dubbed "Theorem 3.1".
Example (Desired Output):
Theorem 1: If x=2, x^3=8.
Proof: Let x=2.
Claim 1.1: For all x and all natural numbers n, x^n = x*x*...*x (n times).
Proof: By induction. QED
(Theorem 1's proof continued) By Claim 1.1, x^3 = 2*2*2 = 8. QED
Additional requirements: Preferably the document class should be "amsart".
Software used: LyX + MiKTeX + BibTeX on Windows 7
My level of LaTeX proficiency: Beginner+