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 Ig being good really-closed Program of SCM+FSA holds
  Ig is parahalting or Ig is_halting_on Initialized s,p
  implies DataPart IExec(Ig ";" j,p,s) = DataPart Exec(j, IExec(Ig,p,s))
proof let Ig be good really-closed Program of SCM+FSA;
  set I = Ig;
  assume
A1: I is parahalting or I is_halting_on Initialized s,p;
  then
A2: for f holds IExec(I ";" j,p,s).f = Exec(j, IExec(I,p,s)).f by Th11;
  for a holds IExec(I ";" j,p,s).a = Exec(j, IExec(I,p,s)).a by A1,Th10;
  hence thesis by A2,SCMFSA_M:2;
end;
