Notation to_nat := N.to_nat.

Lemma QSORaddon : @SORaddon R R0 R1 Rplus Rmult Rminus Ropp (@eq R) Rle (* ring elements *) Q 0%Q 1%Q Qplus Qmult Qminus Qopp (* coefficients *) Qeq_bool Qle_bool Q2R nat to_nat pow.