  We prove a lower bound on the integrated null energy along achronal geodesic
segments using induced gravity on a brane in AdS/CFT. The bound follows from
the assumption that bulk causality respects brane causality, and matches a
bound recently conjectured by Freivogel and Krommydas for semiclassical
gravity. We also prove a more general upper bound on the same quantity that
follows simply from achronality. We check that the lower bound is satisfied in
recent constructions of traversable wormholes, and demonstrate that the bound
is related to causality in the ambient spacetime of the wormhole.
