proposition: Lemma lt_0_IZR : forall n:Z, 0 < IZR n -> (0 < n)%Z.
proof: Proof. intros [| p | p]; simpl; intros H. - destruct (Rlt_irrefl _ H). - now constructor. - destruct (Rlt_not_le _ _ H); unfold IZR; replace R0 with 0 by reflexivity. rewrite <-Ropp_0; apply Ropp_le_contravar, Rle_trans with (1 := Rle_0_1). now apply IPR_ge_1. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField