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

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.