set Mi = Macro (halt SCM+FSA );
hereby :: according to SCMFSA6B:def 4 :: thesis: Macro (halt SCM+FSA ) is parahalting
let s be
State of
SCM+FSA ;
:: thesis: ( (Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )) c= s implies for k being Element of NAT holds (Computation s,k) . (intloc 0 ) = s . (intloc 0 ) )assume A1:
(Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )) c= s
;
:: thesis: for k being Element of NAT holds (Computation s,k) . (intloc 0 ) = s . (intloc 0 )let k be
Element of
NAT ;
:: thesis: (Computation s,k) . (intloc 0 ) = s . (intloc 0 )A2:
insloc 0 in dom ((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 )))
by Th31;
A3:
CurInstr (Computation s,0 ) =
CurInstr s
by AMI_1:13
.=
s . (insloc 0 )
by A1, SF_MASTR:67
.=
((Macro (halt SCM+FSA )) +* (Start-At (insloc 0 ))) . (insloc 0 )
by A1, A2, GRFUNC_1:8
.=
halt SCM+FSA
by Th33
;
s = Computation s,
0
by AMI_1:13;
hence
(Computation s,k) . (intloc 0 ) = s . (intloc 0 )
by A3, AMI_1:52;
:: thesis: verum
end;
thus
Macro (halt SCM+FSA ) is parahalting
by Lm2; :: thesis: verum