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 Program of SCMPDS, J
  being shiftable parahalting Program of SCMPDS,a be Int_position st I
is_closed_on s,P & I is_halting_on 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 Program of SCMPDS,
      J be shiftable parahalting Program of SCMPDS,a be Int_position;
  J is_closed_on IExec(I,P,s),P & J is_halting_on IExec(I,P,s),P
    by SCMPDS_6:20,21;
 hence thesis by SCMPDS_7:30;
end;
