reserve P,P1,P2 for Instruction-Sequence of SCM+FSA;
reserve s for State of SCM+FSA,
  I for Program of SCM+FSA,
  p for Instruction-Sequence of SCM+FSA;

theorem
 for I being really-closed Program of SCM+FSA st s.intloc 0 = 1
 holds I is_halting_on s,p iff I is_halting_on Initialized s,p
proof let I be really-closed Program of SCM+FSA;
  assume s.intloc 0 = 1;
  then DataPart Initialized s = DataPart s by SCMFSA_M:19;
  hence thesis by Th1;
end;
