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Theorem proofobls-backwardsim

⊦ bwsim(IOAut(cstart, cstep, cext), IOAut(astart, astep, aext), t) ↔ (∀ cs. ∃ as. t(cs, as)) ∧ (∀ cs, as. cstart(cs) ∧ t(cs, as) → astart(as)) ∧ (∀ cs, ca, cs0, as0. cstep(cs, ca, cs0) ∧ t(cs0, as0) → (∃ as. move(IOAut(astart, astep, aext))(as, cext !(ca '), as0) ∧ t(cs, as)))