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.