theorem
  pi(X /\ Y,x) c= pi(X,x) /\ pi(Y,x)
proof
  let y be object;
  assume y in pi(X /\ Y,x);
  then consider f such that
A1: f in X /\ Y and
A2: y = f.x by Def6;
A3: f in X by A1,XBOOLE_0:def 4;
A4: f in Y by A1,XBOOLE_0:def 4;
A5: y in pi(X,x) by A2,A3,Def6;
  y in pi(Y,x) by A2,A4,Def6;
  hence thesis by A5,XBOOLE_0:def 4;
end;
