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 ; :: according to AMI_1:def 26,SCMPDS_4:def 10 :: thesis: ( 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 ; :: thesis: ProgramPart s halts_on s
A2: stop (Load ((DataLoc 0 ,0 ) := 0 )) c= s by A1, SCMPDS_4:57;
take 1 ; :: according to AMI_1:def 20 :: thesis: ( 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; :: thesis: (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; :: thesis: verum