  An elegant strategy for proving impossibility results in distributed
computing was introduced in the celebrated FLP consensus impossibility proof.
This strategy is local in nature as at each stage, one configuration of a
hypothetical protocol for consensus is considered, together with future
valencies of possible extensions. This proof strategy has been used in numerous
situations related to consensus, leading one to wonder why it has not been used
in impossibility results of two other well-known tasks: set agreement and
renaming. This paper provides an explanation of why impossibility proofs of
these tasks have been of a global nature. It shows that a protocol can always
solve such tasks locally, in the following sense. Given a configuration and all
its future valencies, if a single successor configuration is selected, then the
protocol can reveal all decisions in this branch of executions, satisfying the
task specification. This result is shown for both set agreement and renaming,
implying that there are no local impossibility proofs for these tasks.
