reserve P,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem
  for s being State of SCM+FSA, I being really-closed Program of SCM+FSA, l
being Nat holds
:::I is_closed_on s,P &
   I is_halting_on s,P
   iff
:::I is_closed_on s +* Start-At(l,SCM+FSA),P+*I &
     I is_halting_on s +* Start-At(l,SCM+FSA),P+*I
proof
  let s be State of SCM+FSA;
  let I be really-closed Program of SCM+FSA;
  let l be Nat;
  DataPart s = DataPart(s +* Start-At(l,SCM+FSA)) by MEMSTR_0:79;
  hence thesis by Th1;
end;
