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 an 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 the two other well-known tasks: *set agreement* and *renaming*. This paper provide an explanation why the proof strategies for showing the impossibility of these tasks have a global nature. We show 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.