  When a quantum system is divided into subsystems, their entanglement
entropies are subject to an inequality known as "strong subadditivity". For a
field theory this inequality can be stated as follows: given any two regions of
space $A$ and $B$, $S(A) + S(B) \ge S(A \cup B) + S(A \cap B)$. Recently, a
method has been found for computing entanglement entropies in any field theory
for which there is a holographically dual gravity theory. In this note we give
a simple geometrical proof of strong subadditivity employing this holographic
prescription.
