reserve i,j,k,n,m for Nat,
        b,b1,b2 for bag of n;

theorem Th5:
  (0,n)-cut (b bag_extend k) = b
proof
  thus (0,n)-cut (b bag_extend k) = (b bag_extend k)|n by Th3,NAT_1:11
    .= b by HILBASIS:def 1;
end;
