reserve x for Int_position,
  n,p0 for Nat;
reserve P,Q,U,V for Instruction-Sequence of SCMPDS;

theorem :: see SCMPDS_7:49
  for s being 0-started State of SCMPDS, I being halt-free parahalting Program
  of SCMPDS , J being shiftable Program of SCMPDS,a be Int_position
   st J is_closed_on IExec(I,P,s),P & J is_halting_on IExec(I,P,s),P
 holds IExec(I ';' J,P,s).a = IExec(J,P,Initialize IExec(I,P,s)).a
proof
  let s be 0-started State of SCMPDS,
      I be halt-free parahalting Program of SCMPDS, J
  be shiftable Program of SCMPDS,a be Int_position;
  I is_closed_on s,P & I is_halting_on s,P by SCMPDS_6:20,21;
  hence thesis by SCMPDS_7:30;
end;
