
theorem
for r being Element of F_Rat st 0 <= r holds r is sum_of_squares
proof
let r be Element of F_Rat;
assume AS: 0 <= r;
r in { r where r is Element of RAT : 0 <= r } by AS,GAUSSINT:def 14;
then r in QS F_Rat by REALALG1:38;
then ex s being Element of F_Rat st s = r & s is sum_of_squares;
hence thesis;
end;
