theorem
  proj2_4(X /\ Y) c= proj2_4 X /\ proj2_4 Y
proof
  proj2_4(X /\ Y) c= proj2_4 X & proj2_4(X /\ Y) c= proj2_4 Y
    by Th17,XBOOLE_1:17;
 hence thesis by XBOOLE_1:19;
end;
