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

theorem Th5: :: see SCMPDS_7:50
  for s being State of SCMPDS, I being halt-free 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 halt-free Program of SCMPDS,j be parahalting
  shiftable Instruction of SCMPDS;
  set Mj = Load j;
A1: Mj is_closed_on IExec(I,P,Initialize s),P &
Mj 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 ';' Mj) is_closed_on s,P & (I ';' Mj) is_halting_on s,P
   by A1,SCMPDS_7:24;
  hence thesis by SCMPDS_4:def 3;
end;
