  Using arguments based on BRST cohomology, the pure spinor formalism for the
superstring in an AdS_5 x S^5 background is proven to be BRST invariant and
conformally invariant at the quantum level to all orders in perturbation
theory. Cohomology arguments are also used to prove the existence of an
infinite set of non-local BRST-invariant charges at the quantum level.
