reserve m,n for Nat,
  a for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1 for Integer,
  loc for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem Th5:
  for I,J being Program of SCMPDS holds Shift(stop J,card I) c=
  stop(I ';' J)
proof
  let I,J be Program of SCMPDS;
  stop(I ';' J) =I ';' J ';' Stop SCMPDS
    .=I ';' (J ';' Stop SCMPDS) by AFINSQ_1:27
    .=I ';' (stop J);
  then stop(I ';' J) = I +* Shift(stop J, card I);
  hence thesis by FUNCT_4:25;
