  We show that the Cantor-Schr\"oder-Bernstein Theorem for homotopy types, or
$\infty$-groupoids holds in the following form: For any two types, if each one
is embedded into the other, then they are equivalent. The argument is developed
in the language of homotopy type theory, or Voevodsky's univalent foundations
(HoTT/UF), and requires classical logic. It follows that the theorem holds in
any boolean $\infty$-topos.
