  Program completion is a translation from the language of logic programs into
the language of first-order theories. Its original definition has been extended
to programs that include integer arithmetic, accept input, and distinguish
between output predicates and auxiliary predicates. For tight programs, that
generalization of completion is known to match the stable model semantics,
which is the basis of answer set programming. We show that the tightness
condition in this theorem can be replaced by a less restrictive "local
tightness" requirement. From this fact we conclude that the proof assistant
anthem-p2p can be used to verify equivalence between locally tight programs.
Under consideration for publication in Theory and Practice of Logic Programming
