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Theorem proofobls-simpleforwardsim

⊦ simplefwsim(IOAut(cstart, cstep, cext), IOAut(astart, astep, aext), r, aabs) ↔ (∀ cs. cstart(cs) → (∃ as. r(as, cs) ∧ astart(as))) ∧ (∀ cs, ca, cs0, as. r(as, cs) ∧ cstep(cs, ca, cs0) → (aabs(ca) = None ⊃ r(as, cs0);∃ as0. astep(as, aabs(ca).get, as0) ∧ r(as0, cs0))) ∧ (∀ ca. (aabs(ca) = None ⊃ cext(ca) = None;cext(ca) = aext(aabs(ca).get)))