  Abstract simulation of one transition system by another is introduced as a
means to simulate a potentially infinite class of similar transition sequences
within a single transition sequence. This is useful for proving confluence
under invariants of a given system, as it may reduce the number of proof cases
to consider from infinity to a finite number. The classical confluence results
for Constraint Handling Rules (CHR) can be explained in this way, using CHR as
a simulation of itself. Using an abstract simulation based on a ground
representation, we extend these results to include confluence under invariant
and modulo equivalence, which have not been done in a satisfactory way before.
