set Ma = Macro (MultBy a,b);
let s be State of ; :: according to AMI_1:def 26,SCMFSA6B:def 3,SCMFSA6C:def 1 :: thesis: ( not (Macro (MultBy a,b)) +* (Start-At (insloc 0 )) c= s or ProgramPart s halts_on s )
assume A22: (Macro (MultBy a,b)) +* (Start-At (insloc 0 )) c= s ; :: thesis: ProgramPart s halts_on s
A23: Macro (MultBy a,b) c= s by A22, 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 A24: IC SCM+FSA in dom (Start-At (insloc 0 )) by TARSKI:def 1;
Start-At (insloc 0 ) c= (Macro (MultBy a,b)) +* (Start-At (insloc 0 )) by FUNCT_4:26;
then Start-At (insloc 0 ) c= s by A22, XBOOLE_1:1;
then A25: IC s = (Start-At (insloc 0 )) . (IC SCM+FSA ) by A24, GRFUNC_1:8
.= insloc 0 by FUNCOP_1:87 ;
then A26: IC (Exec (MultBy a,b),s) = Next (insloc 0 ) by SCMFSA_2:92
.= insloc (0 + 1) ;
insloc 1 in dom (Macro (MultBy a,b)) by SCMFSA6B:32;
then (Macro (MultBy a,b)) . (insloc 1) = s . (insloc 1) by A23, GRFUNC_1:8;
then A27: s . (insloc 1) = halt SCM+FSA by SCMFSA6B:33;
insloc 0 in dom (Macro (MultBy a,b)) by SCMFSA6B:32;
then A28: (Macro (MultBy a,b)) . (insloc 0 ) = s . (insloc 0 ) by A23, GRFUNC_1:8;
Computation s,(0 + 1) = Following (Computation s,0 ) by AMI_1:14
.= Following s by AMI_1:13
.= Exec (MultBy a,b),s by A25, A28, SCMFSA6B:33 ;
then CurInstr (Computation s,1) = halt SCM+FSA by A27, A26, AMI_1:def 13;
hence (ProgramPart s) . (IC (Computation s,1)) = halt SCM+FSA by AMI_1:145; :: thesis: verum