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Theorem proofobls-forwardsim

⊦ fwsim(IOAut(cstart, cstep, cext), IOAut(astart, astep, aext), r) ↔ (∀ cs. cstart(cs) → (∃ as. r(as, cs) ∧ astart(as))) ∧ (∀ cs, ca, cs0, as. r(as, cs) ∧ cstep(cs, ca, cs0) → (∃ as0. move(IOAut(astart, astep, aext))(as, cext !(ca '), as0) ∧ r(as0, cs0)))