theorem
  proj1_4(X /\ Y) c= proj1_4 X /\ proj1_4 Y
proof
  proj1_4(X /\ Y) c= proj1_4 X & proj1_4(X /\ Y) c= proj1_4 Y
   by Th16,XBOOLE_1:17;
 hence thesis by XBOOLE_1:19;
end;
