proposition: 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.
proof: Proof. Proof gen_phiZ_complete Rset Rext Rfield Rgen_phiPOS_not_0. Lemma Rdef_pow_add : forall (x:R) (n m:nat), pow x (n + m) = pow x n * pow x m. Proof. intros x n; elim n; simpl; auto with real. intros n0 H' m; rewrite H'; auto with real. Qed.
imports: Nnat ArithRing Ring Field Rdefinitions Rpow_def Raxioms