let s be State of SCM+FSA ; :: thesis: for a being read-write Int-Location
for I being Program of SCM+FSA st s . (intloc 0 ) = 1 & s . a <> 0 holds
DataPart (IExec (while=0 a,I),s) = DataPart s
let a be read-write Int-Location ; :: thesis: for I being Program of SCM+FSA st s . (intloc 0 ) = 1 & s . a <> 0 holds
DataPart (IExec (while=0 a,I),s) = DataPart s
let I be Program of SCM+FSA ; :: thesis: ( s . (intloc 0 ) = 1 & s . a <> 0 implies DataPart (IExec (while=0 a,I),s) = DataPart s )
set Ins = NAT ;
assume that
A1: s . (intloc 0 ) = 1 and
A2: s . a <> 0 ; :: thesis: DataPart (IExec (while=0 a,I),s) = DataPart s
set WH = while=0 a,I;
set Is = Initialized s;
set Ids = s +* (Initialized (while=0 a,I));
A3: s +* (Initialized (while=0 a,I)) = (Initialized s) +* ((while=0 a,I) +* (Start-At 0 ,SCM+FSA )) by SCMFSA8A:13;
then A4: (while=0 a,I) +* (Start-At 0 ,SCM+FSA ) c= s +* (Initialized (while=0 a,I)) by FUNCT_4:26;
(Initialized s) . a = s . a by SCMFSA6C:3;
then while=0 a,I is_halting_on Initialized s by A2, SCMFSA_9:18;
then A5: ProgramPart (s +* (Initialized (while=0 a,I))) halts_on s +* (Initialized (while=0 a,I)) by A3, SCMFSA7B:def 8;
DataPart (Initialized s) = DataPart (s +* (Initialized (while=0 a,I))) by SCMFSA8B:5;
then A6: (s +* (Initialized (while=0 a,I))) . a = (Initialized s) . a by SCMFSA6A:38
.= s . a by SCMFSA6C:3 ;
NAT misses Int-Locations \/ FinSeq-Locations by SCMFSA_2:13, SCMFSA_2:14, XBOOLE_1:70;
then A7: dom (s | NAT ) misses Int-Locations \/ FinSeq-Locations by SCMFSA8A:3;
thus DataPart (IExec (while=0 a,I),s) = DataPart ((Result (ProgramPart (s +* (Initialized (while=0 a,I)))),(s +* (Initialized (while=0 a,I)))) +* (s | NAT )) by SCMFSA6B:def 1
.= DataPart (Result (ProgramPart (s +* (Initialized (while=0 a,I)))),(s +* (Initialized (while=0 a,I)))) by A7, FUNCT_4:76, SCMFSA_2:127
.= DataPart (Comput (ProgramPart (s +* (Initialized (while=0 a,I)))),(s +* (Initialized (while=0 a,I))),(LifeSpan (ProgramPart (s +* (Initialized (while=0 a,I)))),(s +* (Initialized (while=0 a,I))))) by A5, AMI_1:122
.= DataPart (s +* (Initialized (while=0 a,I))) by A2, A6, A4, Th22
.= DataPart (Initialized s) by SCMFSA8B:5
.= DataPart s by A1, SCMFSA8C:27 ; :: thesis: verum