let p be autonomic halting FinPartState of ; :: 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 such that
A2: p c= s by CARD_3:97;
A3: Relocated p,k is autonomic by A1, Th16;
A4: Relocated p,k is halting by A1, Th13;
ProgramPart s halts_on s by A2, AMI_1:def 26;
then consider j1 being Element of NAT such that
A5: Result s = Computation s,j1 and
A6: CurInstr (Result s) = halt SCM+FSA by AMI_1:def 22;
consider t being State of such that
A7: Relocated p,k c= t by CARD_3:97;
t . (IC (Computation t,j1)) = CurInstr (Computation t,j1) by AMI_1:54
.= IncAddr (CurInstr (Computation s,j1)),k by A1, A2, A7, Th12
.= halt SCM+FSA by A5, A6, SCMFSA_4:8 ;
then A8: Result t = Computation t,j1 by AMI_1:56;
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 A1, A2, A5, A7, A8, 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 A7, A4, A3, AMI_1:def 28 ; :: thesis: verum
reconsider s3 = s +* (DataPart t) as State of ;