reserve x,A for set,
  i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set,
  z for Nat;
reserve y for set;

theorem
  for S being homogeneous J/A-independent standard-ins non empty
     with_halt set,
  I being Element of S st IncAddr(I,k) = halt S holds I = halt S
proof
  let S be homogeneous J/A-independent standard-ins non empty with_halt set,
      I be Element of S;
  assume IncAddr(I,k) = halt S;
  then IncAddr(I,k) = IncAddr(halt S,k) by Th3;
  hence thesis by Th5;
end;
