proposition: Lemma ast_fun_pos : forall n r, (n > 0)%nat -> r > 0 -> (r + 1) ^ n - r > 0.
proof: Proof. intros n r Hn Hr. induction Hn. simpl. ring_simplify. lra. simpl. rewrite Rmult_plus_distr_r. replace 0%R with (0 + 0)%R by intuition. unfold Rminus. rewrite Rplus_assoc. apply Rplus_lt_compat. apply Rmult_gt_0_compat. assumption. apply pow_lt. lra. rewrite Rmult_1_l. apply IHHn. Qed.
imports: Complex Cpow_plus Cpolar Cexp