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; completeness : for every terms <math>T_A^1, T_A^2</math>, if <math>[T_A^2]</math> simulates <math>[T_A^1]</math> then <math>T_A^2</math> simulates <math>T_A^1</math>.
Preservation of simulations is a much stronger property than preservation preservation of observations, which it entails. In turn, it is weaker than a property of preservation of [[bisimulation|bisimulations]]. As in previous cases, soundness is important for compilation, while completeness is useful for testing or proving properties.
=== Preservation of equivalences ===
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