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

theorem :: SCMPDS_7:43
  for s being State of SCMPDS, I being Program of SCMPDS,J being
shiftable parahalting Program of SCMPDS st I is_closed_on s,P
 & I is_halting_on s,P
  holds I ';' J is_closed_on s,P & I ';' J is_halting_on s,P
proof
  let s be State of SCMPDS,I be Program of SCMPDS,J be shiftable parahalting
  Program of SCMPDS;
A1: J is_closed_on IExec(I,P,Initialize s),P &
J is_halting_on IExec(I,P,Initialize s),P
 by SCMPDS_6:20,21;
  assume
  I is_closed_on s,P & I is_halting_on s,P;
  hence thesis by A1,SCMPDS_7:24;
end;
