proposition: Lemma eq_IZR_R0 : forall n:Z, IZR n = 0 -> n = 0%Z.
proof: Proof. intros [| p | p]; unfold IZR; simpl; intros H; try easy. - exfalso; apply (Rlt_not_eq 0 (IPR p)); try easy; apply IPR_gt_0. - exfalso; apply (Rlt_not_eq 0 (IPR p)); try apply IPR_gt_0; symmetry. replace R0 with 0 in H by reflexivity; rewrite <-Ropp_0 in H. now apply Ropp_eq_reg. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField