reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, b for Element of E^omega;
reserve i, k, l, kl, m, n, mn for Nat;

theorem Th3:
  m < n implies ex k st m + k = n & k > 0
proof
  assume m < n;
  then (ex k st m + k = n )& m - m < n - m by NAT_1:10,XREAL_1:14;
  hence thesis;
end;
