reserve i,j,x,y for object,
  f,g for Function;
reserve T,T1 for finite Tree,
  t,p for Element of T,
  t1 for Element of T1;

theorem
  for f, g being Function holds
  dom f,dom g are_equipotent iff f,g are_equipotent
proof
  let f, g be Function;
A1: card f = card dom f & card g = card dom g by CARD_1:62;
  hereby
    assume dom f,dom g are_equipotent;
    then card dom f = card dom g by CARD_1:5;
    hence f,g are_equipotent by A1,CARD_1:5;
  end;
  assume f,g are_equipotent;
  then card f = card g by CARD_1:5;
  hence thesis by A1,CARD_1:5;
end;
