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

theorem
  X \ (Y \+\ Z) = X \ (Y \/ Z) \/ X /\ Y /\ Z
proof
  thus X \ (Y \+\ Z) = X \ ((Y \/ Z) \ Y /\ Z) by Lm5
    .= X \ (Y \/ Z) \/ X /\ (Y /\ Z) by Th52
    .= X \ (Y \/ Z) \/ X /\ Y /\ Z by Th16;
end;
