theorem
  for f1 being Function of X1,Y1 for f2 being Function of X2,Y2 st (Y1 =
{} implies X1 = {}) & (Y2 = {} implies X2 = {}) holds [:f1,f2:] = <:f1*pr1(X1,
  X2),f2*pr2(X1,X2):>
proof
  let f1 be Function of X1,Y1;
  let f2 be Function of X2,Y2;
  assume ( Y1 = {} implies X1 = {})&( Y2 = {} implies X2 = {});
  then dom f1 = X1 & dom f2 = X2 by FUNCT_2:def 1;
  hence thesis by Th66;
end;
