set SA0 = Start-At (inspos 0 );
set ii = (DataLoc 0 ,0 ) := 0 ;
set m0 = stop (Load ((DataLoc 0 ,0 ) := 0 ));
set m1 = Initialized (stop (Load ((DataLoc 0 ,0 ) := 0 )));
let s be State of ; AMI_1:def 26,SCMPDS_4:def 10 ( not Initialized (stop (Load ((DataLoc 0 ,0 ) := 0 ))) c= s or ProgramPart s halts_on s )
assume A1:
Initialized (stop (Load ((DataLoc 0 ,0 ) := 0 ))) c= s
; ProgramPart s halts_on s
A2:
stop (Load ((DataLoc 0 ,0 ) := 0 )) c= s
by A1, SCMPDS_4:57;
take
1
; AMI_1:def 20 ( IC (Computation s,1) in dom (ProgramPart s) & (ProgramPart s) . (IC (Computation s,1)) = halt SCMPDS )
IC (Computation s,1) in NAT
by AMI_1:def 4;
hence
IC (Computation s,1) in dom (ProgramPart s)
by AMI_1:143; (ProgramPart s) . (IC (Computation s,1)) = halt SCMPDS
dom (Start-At (inspos 0 )) = {(IC SCMPDS )}
by FUNCOP_1:19;
then A3:
IC SCMPDS in dom (Start-At (inspos 0 ))
by TARSKI:def 1;
Start-At (inspos 0 ) c= Initialized (stop (Load ((DataLoc 0 ,0 ) := 0 )))
by FUNCT_4:26;
then
Start-At (inspos 0 ) c= s
by A1, XBOOLE_1:1;
then A4: IC s =
(Start-At (inspos 0 )) . (IC SCMPDS )
by A3, GRFUNC_1:8
.=
inspos 0
by FUNCOP_1:87
;
then A5: IC (Exec ((DataLoc 0 ,0 ) := 0 ),s) =
Next (inspos 0 )
by SCMPDS_2:57
.=
inspos (0 + 1)
;
inspos 1 in dom (stop (Load ((DataLoc 0 ,0 ) := 0 )))
by Th9;
then
(stop (Load ((DataLoc 0 ,0 ) := 0 ))) . (inspos 1) = s . (inspos 1)
by A2, GRFUNC_1:8;
then A6:
s . (inspos 1) = halt SCMPDS
by Th10;
inspos 0 in dom (stop (Load ((DataLoc 0 ,0 ) := 0 )))
by Th9;
then A7:
(stop (Load ((DataLoc 0 ,0 ) := 0 ))) . (inspos 0 ) = s . (inspos 0 )
by A2, GRFUNC_1:8;
Computation s,(0 + 1) =
Following (Computation s,0 )
by AMI_1:14
.=
Following s
by AMI_1:13
.=
Exec ((DataLoc 0 ,0 ) := 0 ),s
by A4, A7, Th10
;
then
CurInstr (Computation s,1) = halt SCMPDS
by A6, A5, AMI_1:def 13;
hence
(ProgramPart s) . (IC (Computation s,1)) = halt SCMPDS
by AMI_1:145; verum