set Ma = Macro (AddTo (a,b));
let s be State of SCM+FSA; :: according to EXTPRO_1:def 10,SCMFSA6B:def 3,SCMFSA6C:def 1 :: thesis:
assume A8: (Macro (AddTo (a,b))) +* (Start-At (0,SCM+FSA)) c= s ; :: thesis:
A9: Macro (AddTo (a,b)) c= s by A8, SCMFSA6B:5;
take 1 ; :: according to EXTPRO_1:def 7 :: thesis:
IC (Comput ((ProgramPart s),s,1)) in NAT ;
hence IC (Comput ((ProgramPart s),s,1)) in dom (ProgramPart s) by COMPOS_1:34; :: thesis:
dom (Start-At (0,SCM+FSA)) = {(IC SCM+FSA)} by FUNCOP_1:19;
then A10: IC SCM+FSA in dom (Start-At (0,SCM+FSA)) by TARSKI:def 1;
Start-At (0,SCM+FSA) c= (Macro (AddTo (a,b))) +* (Start-At (0,SCM+FSA)) by FUNCT_4:26;
then Start-At (0,SCM+FSA) c= s by A8, XBOOLE_1:1;
then A11: IC s = (Start-At (0,SCM+FSA)) . (IC SCM+FSA) by A10, GRFUNC_1:8
.= 0 by FUNCOP_1:87 ;
then A12: IC (Exec ((AddTo (a,b)),s)) = succ 0 by SCMFSA_2:90
.= 0 + 1 ;
1 in dom (Macro (AddTo (a,b))) by SCMFSA6B:32;
then (Macro (AddTo (a,b))) . 1 = s . 1 by A9, GRFUNC_1:8;
then A13: s . 1 = halt SCM+FSA by COMPOS_1:148, SCMFSA6B:33;
0 in dom (Macro (AddTo (a,b))) by SCMFSA6B:32;
then A14: (Macro (AddTo (a,b))) . 0 = s . 0 by A9, 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 ((AddTo (a,b)),s) by A11, A14, Y, COMPOS_1:148, SCMFSA6B:33 ;
then CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA by A13, A12, Z, NX, AMI_1:def 13;
hence CurInstr ((ProgramPart s),(Comput ((ProgramPart s),s,1))) = halt SCM+FSA ; :: thesis: