let p be autonomic halting FinPartState of SCM+FSA ; :: thesis: ( IC SCM+FSA in dom p implies for k being Element of NAT holds DataPart (Result p) = DataPart (Result (Relocated p,k)) )
assume A1: IC SCM+FSA in dom p ; :: thesis: for k being Element of NAT holds DataPart (Result p) = DataPart (Result (Relocated p,k))
let k be Element of NAT ; :: thesis: DataPart (Result p) = DataPart (Result (Relocated p,k))
consider s being State of SCM+FSA such that
A2: p c= s by CARD_3:97;
s is halting by A2, AMI_1:def 26;
then consider j1 being Element of NAT such that
A3: Result s = Computation s,j1 and
A4: CurInstr (Result s) = halt SCM+FSA by AMI_1:def 22;
consider t being State of SCM+FSA such that
A5: Relocated p,k c= t by CARD_3:97;
reconsider s3 = s +* (DataPart t) as State of SCM+FSA ;
t . (IC (Computation t,j1)) = CurInstr (Computation t,j1) by AMI_1:54
.= IncAddr (CurInstr (Computation s,j1)),k by A1, A2, A5, Th12
.= halt SCM+FSA by A3, A4, SCMFSA_4:8 ;
then A7: Result t = Computation t,j1 by AMI_1:56;
A9: ( Relocated p,k is halting & Relocated p,k is autonomic ) by A1, Th13, Th16;
thus DataPart (Result p) = DataPart ((Result s) | (dom p)) by A2, AMI_1:def 28
.= (Result s) | ((dom p) /\ (Int-Locations \/ FinSeq-Locations )) by RELAT_1:100, SCMFSA_2:127
.= (Result s) | (dom (DataPart p)) by RELAT_1:90, SCMFSA_2:127
.= (Result t) | (dom (DataPart (Relocated p,k))) by A3, A7, A1, A2, A5, Th12
.= (Result t) | ((dom (Relocated p,k)) /\ (Int-Locations \/ FinSeq-Locations )) by RELAT_1:90, SCMFSA_2:127
.= DataPart ((Result t) | (dom (Relocated p,k))) by RELAT_1:100, SCMFSA_2:127
.= DataPart (Result (Relocated p,k)) by A5, A9, AMI_1:def 28 ; :: thesis: verum