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

theorem
  (X \+\ Y) \ Z = (X \ (Y \/ Z)) \/ (Y \ (X \/ Z))
proof
  thus (X \+\ Y) \ Z = (X \ Y \ Z) \/ (Y \ X \ Z) by Th42
    .= (X \ (Y \/ Z)) \/ (Y \ X \ Z) by Th41
    .= (X \ (Y \/ Z)) \/ (Y \ (X \/ Z)) by Th41;
end;
