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 ## Checklist 
 
-- [ ] Item 1
-- [ ] Item 2
-- [ ] Item 3
+- [ ] Introduce HJ-simulation in relator-form, show uniqness of wittnesses.
+- [ ] Prove a general theorem that symmetric simulation for symmetrized relator yields similarity that is sound and complete for behavioral equivalence (use "Relators and Notions of Simulation Revisited" soundness and compteleness criterion).
+- [ ] Elaborate this for powerset
+- [ ] When is symmetrized relator the Barr relator (definition is in "Relators and Notions of Simulation Revisited")?
+- [ ] At least, try to prove it for the Jacobs-Hughes relator
+- [ ] Introduce notions of simulation, diverging from HJ-simulation. Do we need two of them (with normalization and without)? How are all of them related?
+- [x] Can we separate Hughes-Jacobs relator from one-sided lax relator?
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