reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;

theorem Th3:
  for I,J being Program of SCMPDS holds
   stop I +* stop (I ';' J) = stop (I ';' J)
proof
  let I,J be Program of SCMPDS;
  set sI=stop I, IsI=sI, sIJ=stop (I ';' J), IsIJ= sIJ;
  dom sI c= dom sIJ by Th2;
  hence thesis by FUNCT_4:19;
end;
