set Ma = Macro (a := b);
let s be State of ; :: according to AMI_1:def 26,SCMFSA6B:def 3,SCMFSA6C:def 1 :: thesis: ( not (Macro (a := b)) +* (Start-At (insloc 0 )) c= s or ProgramPart s halts_on s )
assume A1: (Macro (a := b)) +* (Start-At (insloc 0 )) c= s ; :: thesis: ProgramPart s halts_on s
A2: Macro (a := b) c= s by A1, SCMFSA6B:5;
take 1 ; :: according to AMI_1:def 20 :: thesis: ( IC (Computation s,1) in dom (ProgramPart s) & (ProgramPart s) . (IC (Computation s,1)) = halt SCM+FSA )
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 SCM+FSA
dom (Start-At (insloc 0 )) = {(IC SCM+FSA )} by FUNCOP_1:19;
then A3: IC SCM+FSA in dom (Start-At (insloc 0 )) by TARSKI:def 1;
Start-At (insloc 0 ) c= (Macro (a := b)) +* (Start-At (insloc 0 )) by FUNCT_4:26;
then Start-At (insloc 0 ) c= s by A1, XBOOLE_1:1;
then A4: IC s = (Start-At (insloc 0 )) . (IC SCM+FSA ) by A3, GRFUNC_1:8
.= insloc 0 by FUNCOP_1:87 ;
then A5: IC (Exec (a := b),s) = Next (insloc 0 ) by SCMFSA_2:89
.= insloc (0 + 1) ;
insloc 1 in dom (Macro (a := b)) by SCMFSA6B:32;
then (Macro (a := b)) . (insloc 1) = s . (insloc 1) by A2, GRFUNC_1:8;
then A6: s . (insloc 1) = halt SCM+FSA by SCMFSA6B:33;
insloc 0 in dom (Macro (a := b)) by SCMFSA6B:32;
then A7: (Macro (a := b)) . (insloc 0 ) = s . (insloc 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 (a := b),s by A4, A7, SCMFSA6B:33 ;
then CurInstr (Computation s,1) = halt SCM+FSA by A6, A5, AMI_1:def 13;
hence (ProgramPart s) . (IC (Computation s,1)) = halt SCM+FSA by AMI_1:145; :: thesis: verum