We present a new algorithm for generating a formal proof that an access request satisfies accesscontrol
policy, for use in logic-based access-control frameworks. Our algorithm is tailored to settings
where credentials needed to complete a proof might need to be obtained from, or reactively created
by, distant components in a distributed system. In such contexts, our algorithm substantially improves
upon previous proposals in both computation and communication costs, and better guides users to create
the most appropriate credentials in those cases where needed credentials do not yet exist. At the same
time, our algorithm offers strictly superior proving ability, in the sense that it finds a proof in every
case that previous approaches would (and more). We detail our algorithm and empirically evaluate an
implementation of it using policies in active use in a testbed at our institution for experimenting with
access-control technologies.