TITLE: A proof of Theorem 9.2.12. in the Gompf-Stipsicz
QUESTION [6 upvotes]: 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.

REPLY [5 votes]: The weaker version is a result due to Wall:

C.T.C. Wall,
  On simply connected 4-manifolds,
  J. London Math. Soc., 39 (1964), 141–149

A stronger statement has been proven by Kreck (who also gives some references), but I don't know about the original reference Gompf and Stipsicz were thinking about.

Matthias Kreck,
  h-cobordisms between 1-connected 4-manifolds
  Geom. Topol., 5 (2001), 1-6