set m = Macro (halt SCM+FSA );
set m1 = Initialized (Macro (halt SCM+FSA ));
let s be State of SCM+FSA ; :: according to AMI_1:def 26,SCM_HALT:def 2 :: thesis: ( not Initialized (Macro (halt SCM+FSA )) c= s or s is halting )
assume A1:
Initialized (Macro (halt SCM+FSA )) c= s
; :: thesis: s is halting
A3:
Initialized (Macro (halt SCM+FSA )) = (Macro (halt SCM+FSA )) +* (((intloc 0 ) .--> 1) +* (Start-At (insloc 0 )))
by FUNCT_4:15;
dom (Start-At (insloc 0 )) = {(IC SCM+FSA )}
by FUNCOP_1:19;
then A4:
IC SCM+FSA in dom (Start-At (insloc 0 ))
by TARSKI:def 1;
then A5:
IC SCM+FSA in dom (Initialized (Macro (halt SCM+FSA )))
by FUNCT_4:13;
A7:
(Macro (halt SCM+FSA )) . (insloc 0 ) = halt SCM+FSA
by FUNCT_4:66;
A8:
Macro (halt SCM+FSA ) c= Initialized (Macro (halt SCM+FSA ))
by SCMFSA6A:26;
dom (Macro (halt SCM+FSA )) = {(insloc 0 ),(insloc 1)}
by FUNCT_4:65;
then A9:
insloc 0 in dom (Macro (halt SCM+FSA ))
by TARSKI:def 2;
then A10:
insloc 0 in dom (Initialized (Macro (halt SCM+FSA )))
by A3, FUNCT_4:13;
A11: IC (Initialized (Macro (halt SCM+FSA ))) =
(Initialized (Macro (halt SCM+FSA ))) . (IC SCM+FSA )
by A5, AMI_1:def 43
.=
(Start-At (insloc 0 )) . (IC SCM+FSA )
by A4, 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 (Initialized (Macro (halt SCM+FSA ))))
by A1, A5, AMI_1:97
.=
(Initialized (Macro (halt SCM+FSA ))) . (insloc 0 )
by A1, A10, A11, GRFUNC_1:8
.=
halt SCM+FSA
by A7, A8, A9, GRFUNC_1:8
; :: thesis: verum