LyX ⇒ Numbering a nested Theorem

[Itai]

How to accomplish the following output under the amsart document class (AMS Article)? Note the hierarchical numbering of the nested theorem.

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

Thanks.