theorem
  for f1,f2 being Function of X,D1 for g1,g2 being Function of X,D2 st
  <:f1,g1:> = <:f2,g2:> holds f1 = f2 & g1 = g2
proof
  let f1,f2 be Function of X,D1;
  let g1,g2 be Function of X,D2;
A1: dom g1 = X & dom g2 = X by FUNCT_2:def 1;
  dom f1 = X & dom f2 = X by FUNCT_2:def 1;
  hence thesis by A1,Th54;
end;
