  Abstract interpretation is a method to automatically find invariants of
programs or pieces of code whose semantics is given via least fixed-points.
Up-to techniques have been introduced as enhancements of coinduction, an
abstract principle to prove properties expressed via greatest fixed-points.
  While abstract interpretation is always sound by definition, the soundness of
up-to techniques needs some ingenuity to be proven. For completeness, the
setting is switched: up-to techniques are always complete, while abstract
domains are not.
  In this work we show that, under reasonable assumptions, there is an evident
connection between sound up-to techniques and complete abstract domains.
