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

theorem
  X misses Y implies X /\ (Y \/ Z) = X /\ Z
proof
  assume X misses Y;
  then X /\ Y = {};
  hence X /\ (Y \/ Z) = {} \/ X /\ Z by Th23
    .= X /\ Z;
end;
