  Quantum Focusing is a powerful conjecture, which plays a key role in the
current proofs of many well-known quantum gravity theorems, including various
consistency conditions, and causality constraints in AdS/CFT. I conjecture a
(weaker) restricted quantum focusing, which I argue is sufficient to derive all
known essential implications of quantum focusing. Subject to a technical
assumption, I prove this conjecture on brane-world semiclassical gravity
theories which are holographically dual to Einstein gravity in a higher
dimensional anti-de Sitter spacetime.
