# A proof of Theorem 9.2.12. in the Gompf-Stipsicz

I'm seeking for a proof of Theorem 9.2.12. in the Gompf-Stipsicz "4-Manifolds and Kirby Calculus" (for the statement, see the following image). But the textbook omits any proofs and only gives a weaker version (Theorem 9.2.13.). My question is:

How can we find a proof of the theorem?

Any references will be fine. Thank you for your help.

• See, e.g., The Wide World of 4-Manifolds by A. Scorpan (google books) for a recent exposition of the Wall reference and its corollaries (p. 155, linked). Jul 10, 2016 at 9:20

• @Golla Yes, I have already learned that, if two simply-connected closed 4-manifolds have the same intersection form, then they are h-cobordant. But I really need now is "functorial h-cobordism" (satisfying $\varphi_W=\varphi$ , see the attached image). Where can we find this statement in the Wall's paper? Jul 11, 2016 at 1:47