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