Definition Rsrt : ring_theory R0 R1 Rplus Rmult Rminus Ropp (@eq R).

(* Specifications: *)
Lemma Rsor : SOR R0 R1 Rplus Rmult Rminus Ropp (@eq R) Rle Rlt.
Lemma Rinv_1 : forall x, x * / 1 = x.
Lemma Qeq_true : forall x y, Qeq_bool x y = true -> Q2R x = Q2R y.
Lemma Qeq_false : forall x y, Qeq_bool x y = false -> Q2R x <> Q2R y.
Lemma Qle_true : forall x y : Q, Qle_bool x y = true -> Q2R x <= Q2R y.
Lemma Q2R_0 : Q2R 0 = 0.
Lemma Q2R_1 : Q2R 1 = 1.
Lemma Q2R_inv_ext : forall x, Q2R (/ x) = (if Qeq_bool x 0 then 0 else / Q2R x).