reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;

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;
