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

theorem
  (X /\ Y) \/ (X /\ Z) c= Y \/ Z
proof
  now
    let x be object;
    assume x in (X /\ Y) \/ (X /\ Z);
    then x in (X /\ Y) or x in (X /\ Z) by XBOOLE_0:def 3;
    then x in X & x in Y or x in X & x in Z by XBOOLE_0:def 4;
    hence x in Y \/ Z by XBOOLE_0:def 3;
  end;
  hence thesis;
end;
