reserve p,P,P1,P2 for Instruction-Sequence of SCM+FSA;
reserve s, S for State of SCM+FSA,
  I, J for Program of SCM+FSA,
  Ig for good Program of SCM+FSA,
  i for good sequential Instruction of SCM+FSA,
  j for sequential Instruction of SCM+FSA,
  a, b for Int-Location,
  f for FinSeq-Location;

theorem
 for J being really-closed Program of SCM+FSA holds
  J is parahalting or J is_halting_on Exec(i, Initialized s),p
implies
  DataPart IExec(i ";" J,p,s) = DataPart IExec(J,p,Exec(i,Initialized s))
proof let J be really-closed Program of SCM+FSA;
  assume
A1: J is parahalting or J is_halting_on Exec(i, Initialized s),p;
  then
A2: for f holds IExec(i ";" J,p,s).f = IExec(J,p,Exec(i,Initialized s)).f
by Th14;
  for a holds IExec(i ";" J,p,s).a
   = IExec(J,p,Exec(i,Initialized s)).a by A1,Th13;
  hence thesis by A2,SCMFSA_M:2;
end;
