Patching formulas for spin polynomials, and a proof of the Van de Ven conjecture

In the present paper some formulas for spin invariants of a connected sum of an arbitrary four-dimensional manifold $X$ with $b_2^+(X)>0$ and $\overline{\mathbb C\mathbb P^2}$ in terms of spin invariants of $X$ are obtained, and the results are used to get a proof of the Van de Ven conjecture.