theorem
  pi(X,x) \+\ pi(Y,x) c= pi(X \+\ Y,x)
proof
A1: pi(X,x) \ pi(Y,x) c= pi(X\Y,x) by Th18;
A2: pi(Y,x) \ pi(X,x) c= pi(Y\X,x) by Th18;
  pi(X\Y,x) \/ pi(Y\X,x) = pi((X\Y) \/ (Y\X),x) by Th16;
  hence thesis by A1,A2,XBOOLE_1:13;
end;
