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

theorem
  (X /\ Z) \+\ (Y /\ Z) = (X \+\ Y) /\ Z
proof
  thus (X /\ Z) \+\ (Y /\ Z) = ((X \ Y) /\ Z) \/ ((Y /\ Z) \ (X /\ Z)) by Th111
    .= ((X \ Y) /\ Z) \/ ((Y \ X) /\ Z) by Th111
    .= (X \+\ Y) /\ Z by Th23;
end;
