red; intros.
specialize (Rgen_phiPOS x).
rewrite H; intro.
apply (Rlt_asym 0 0); trivial.
Qed.

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.