theorem
  (X \/ Y) \/ Z = (X \/ Z) \/ (Y \/ Z)
proof
  (X \/ Y) \/ Z = X \/ ((Z \/ Z) \/ Y) by Th4
    .= X \/ (Z \/ (Z \/ Y)) by Th4
    .= (X \/ Z) \/ (Y \/ Z) by Th4;
  hence thesis;
end;
