  The Ryu-Takayanagi formula implies many general properties of entanglement
entropies in holographic theories. We review the known properties, such as
continuity, strong subadditivity, and monogamy of mutual information, and fill
in gaps in some of the previously-published proofs. We also add a few new
properties, including: properties of the map from boundary regions to bulk
regions implied by the RT formula, such as monotonicity; conditions under which
subadditivity-type inequalities are saturated; and an inequality concerning
reflection-symmetric states. We attempt to draw lessons from these properties
about the structure of the reduced density matrix in holographic theories.
