set m = Macro (halt SCM+FSA );
set m1 = (Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ));
let s be State of SCM+FSA ; :: according to AMI_1:def 26,SCMFSA6B:def 3 :: thesis: ( not (Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )) c= s or s is halting )
assume A1:
(Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )) c= s
; :: thesis: s is halting
A2:
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;
then A4:
IC SCM+FSA in dom ((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )))
by FUNCT_4:13;
A6:
(Macro (halt SCM+FSA )) . (insloc 0 ) = halt SCM+FSA
by FUNCT_4:66;
A7:
dom (Macro (halt SCM+FSA )) = {(insloc 0 ),(insloc 1)}
by FUNCT_4:65;
then
dom (Macro (halt SCM+FSA )) misses dom (Start-At (insloc 0 ))
by XBOOLE_0:def 7;
then A9:
Macro (halt SCM+FSA ) c= (Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))
by FUNCT_4:33;
dom (Macro (halt SCM+FSA )) = {(insloc 0 ),(insloc 1)}
by FUNCT_4:65;
then A10:
insloc 0 in dom (Macro (halt SCM+FSA ))
by TARSKI:def 2;
then A11:
insloc 0 in dom ((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )))
by FUNCT_4:13;
A12: IC ((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))) =
((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))) . (IC SCM+FSA )
by A4, AMI_1:def 43
.=
(Start-At (insloc 0 )) . (IC SCM+FSA )
by A3, FUNCT_4:14
.=
insloc 0
by FUNCOP_1:87
;
take
0
; :: according to AMI_1:def 20 :: thesis: CurInstr (Computation s,0 ) = halt SCM+FSA
thus CurInstr (Computation s,0 ) =
CurInstr s
by AMI_1:13
.=
s . (IC ((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))))
by A1, A4, AMI_1:97
.=
((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))) . (insloc 0 )
by A1, A11, A12, GRFUNC_1:8
.=
halt SCM+FSA
by A6, A9, A10, GRFUNC_1:8
; :: thesis: verum