reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X \/ Y = X \+\ (Y \ X)
proof
A1: Y \ X \ X = Y \ (X \/ X) by Th41
    .= Y \ X;
  X \ (Y \ X) = (X \ Y) \/ X /\ X by Th52
    .= X by Th12,Th36;
  hence thesis by A1,Th39;
end;
