set Ma = Macro (b := (f,a));
let s be State of SCM+FSA; :: according to EXTPRO_1:def 10,SCMFSA6B:def 3,SCMFSA6C:def 1 :: thesis: ( not (Macro (b := (f,a))) +* (Start-At (0,SCM+FSA)) c= s or ProgramPart s halts_on s )
assume A36: (Macro (b := (f,a))) +* (Start-At (0,SCM+FSA)) c= s ; :: thesis: ProgramPart s halts_on s
A37: Macro (b := (f,a)) c= s by A36, SCMFSA6B:5;
take 1 ; :: according to EXTPRO_1:def 7 :: thesis: ( IC (Comput ((ProgramPart s),s,1)) in proj1 (ProgramPart s) & CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA )
IC (Comput ((ProgramPart s),s,1)) in NAT ;
hence IC (Comput ((ProgramPart s),s,1)) in dom (ProgramPart s) by COMPOS_1:34; :: thesis: CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA
dom (Start-At (0,SCM+FSA)) = {(IC SCM+FSA)} by FUNCOP_1:19;
then A38: IC SCM+FSA in dom (Start-At (0,SCM+FSA)) by TARSKI:def 1;
Start-At (0,SCM+FSA) c= (Macro (b := (f,a))) +* (Start-At (0,SCM+FSA)) by FUNCT_4:26;
then Start-At (0,SCM+FSA) c= s by A36, XBOOLE_1:1;
then A39: IC s = (Start-At (0,SCM+FSA)) . (IC SCM+FSA) by A38, GRFUNC_1:8
.= 0 by FUNCOP_1:87 ;
then A40: IC (Exec ((b := (f,a)),s)) = succ 0 by SCMFSA_2:98
.= 0 + 1 ;
1 in dom (Macro (b := (f,a))) by SCMFSA6B:32;
then (Macro (b := (f,a))) . 1 = s . 1 by A37, GRFUNC_1:8;
then A41: s . 1 = halt SCM+FSA by COMPOS_1:148, SCMFSA6B:33;
0 in dom (Macro (b := (f,a))) by SCMFSA6B:32;
then A42: (Macro (b := (f,a))) . 0 = s . 0 by A37, GRFUNC_1:8;
Y: (ProgramPart s) /. (IC s) = s . (IC s) by COMPOS_1:38;
Z: (ProgramPart (Comput ((ProgramPart s),s,1))) /. (IC (Comput ((ProgramPart s),s,1))) = (Comput ((ProgramPart s),s,1)) . (IC (Comput ((ProgramPart s),s,1))) by COMPOS_1:38;
NX: ProgramPart s = ProgramPart (Comput ((ProgramPart s),s,1)) by AMI_1:123;
Comput ((ProgramPart s),s,(0 + 1)) = Following ((ProgramPart s),(Comput ((ProgramPart s),s,0))) by EXTPRO_1:4
.= Following ((ProgramPart s),s) by EXTPRO_1:3
.= Exec ((b := (f,a)),s) by A39, A42, Y, COMPOS_1:148, SCMFSA6B:33 ;
then CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA by A41, A40, Z, NX, AMI_1:def 13;
hence CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA ; :: thesis: verum