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Theorem proofobls-branchingforwardsim

⊦ bfwsim(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) → (cext(ca) = None ⊃ r(as, cs0) ;∃ asl, aal, aa, as1. frag*(IOAut(astart, astep, aext))(asl, aal) ∧ aext !(aal) = [] ∧ asl.head = as ∧ (∀ as. as ∈ asl → r(as, cs)) ∧ astep(asl.last, aa, as1) ∧ cext(ca) = aext(aa) ∧ r(as1, cs0) ))