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
  parahalting shiftable Instruction 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
  Instruction of SCMPDS;
A1: Load j is_closed_on IExec(I,P,Initialize s),P &
Load 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;
  then I ';' Load j is_closed_on s,P & I ';' Load j is_halting_on s,P by A1,
SCMPDS_7:24;
  hence thesis by SCMPDS_4:def 3;
end;
