theorem
  proj1 X \+\ proj1 Y c= proj1(X \+\ Y)
proof
  proj1 X \ proj1 Y c= proj1(X \ Y) & proj1 Y \ proj1 X c= proj1(Y \ X)
     by Th25;
  then proj1 X \+\ proj1 Y c= proj1(X\Y) \/ proj1(Y\X) by XBOOLE_1:13;
 hence thesis by Th23;
end;
