reserve m,n for Nat,
  I for Program of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  a for Int-Location,
  f for FinSeq-Location,
  p,p1,p2 for Instruction-Sequence of SCM+FSA;

theorem Th7:
  for I being keepInt0_1 InitHalting Program of SCM+FSA holds
  IExec(I,p,s).intloc 0 = 1
proof
  let I be keepInt0_1 InitHalting Program of SCM+FSA;
A1:  iS c= Initialized s by FUNCT_4:25;
A2: I c= p+*I by FUNCT_4:25;
  then p+*I halts_on Initialized s by Def1,A1;
  then
A3: iS c= Initialized s &
 ex n st Result(p +* I,Initialized s) =
  Comput(p +* I,Initialized s,n) &
   CurInstr(p+*I,Result(p+*I,Initialized s))
    = halt SCM+FSA by EXTPRO_1:def 9,FUNCT_4:25;
  thus IExec(I,p,s).intloc 0 = (Result(p+*I,Initialized s)).intloc 0
   by SCMFSA6B:def 1
    .= 1 by A3,A2,Def2;
end;
