Wall's stable realization for diffeomorphisms of definite 4-manifolds

Let $X$ be a smooth simply connected closed 4-manifold with definite intersection form. We show that any automorphism of the intersection form of $X$ is realized by a diffeomorphism of $X\mathrm{\#}{S}^2\times S^2$. This extends and completes Wall’s foundational result from 1964.