  The bisimulation proof method can be enhanced by employing `bisimulations
up-to' techniques. A comprehensive theory of such enhancements has been
developed for first-order (i.e., CCS-like) labelled transition systems (LTSs)
and bisimilarity, based on abstract fixed-point theory and compatible
functions.
  We transport this theory onto languages whose bisimilarity and LTS go beyond
those of first-order models. The approach consists in exhibiting fully abstract
translations of the more sophisticated LTSs and bisimilarities onto the
first-order ones. This allows us to reuse directly the large corpus of up-to
techniques that are available on first-order LTSs. The only ingredient that has
to be manually supplied is the compatibility of basic up-to techniques that are
specific to the new languages. We investigate the method on the pi-calculus,
the lambda-calculus, and a (call-by-value) lambda-calculus with references.
