  We provide a new and concise proof of the existence of suprema in the Cuntz
semigroup using the open projection picture of the Cuntz semigroup initiated by
Ortega, Rordam and Thiel. Our argument is based on the observation that the
supremum of a countable set of open projections in the bidual of a C*-algebra A
is again open and corresponds to the generated hereditary sub-C*-algebra of A.
