Notation Rset := (Eqsth R).Notation Rext := (Eq_ext Rplus Rmult Ropp).

(* Specifications: *)
Lemma Rlt_0_2 : 0 < 2.
Lemma Rgen_phiPOS : forall x, InitialRing.gen_phiPOS1 1 Rplus Rmult x > 0.
Lemma Rgen_phiPOS_not_0 : forall x, InitialRing.gen_phiPOS1 1 Rplus Rmult x <> 0.
Lemma Zeq_bool_complete : forall x y, InitialRing.gen_phiZ 0%R 1%R Rplus Rmult Ropp x = InitialRing.gen_phiZ 0%R 1%R Rplus Rmult Ropp y -> Zeq_bool x y = true.
Lemma Rdef_pow_add : forall (x:R) (n m:nat), pow x (n + m) = pow x n * pow x m.
Lemma R_power_theory : power_theory 1%R Rmult (@eq R) N.to_nat pow.