  We prove that the double branched cover of a twist-roll spun knot in $S^4$ is
smoothly preserved when four twists are added, and that the double branched
cover of a twist-roll spun knot connected sum with a trivial projective plane
is preserved after two twists are added. As a consequence, we conclude that a
family of homotopy $\mathbb{CP}^2$s recently constructed by Miyazawa are each
diffeomorphic to $\mathbb{CP}^2$.
