proposition: Lemma Bn_growing : forall n, (Bn n) <= (Bn (S n)).
proof: Proof. intros n; induction n; simpl. unfold fp; destruct f. apply Rplus_le_le_0_compat. apply Rle_refl. apply pow_le; apply Rle_0_inv_2. rewrite Rplus_0_l; apply Rle_refl. unfold fp. assert (H : 0 <= (/2) ^ (S (S n))). apply pow_le; apply Rle_0_inv_2. do 2 destruct f; repeat rewrite Rplus_assoc. apply Rplus_le_compat_l. pattern ((/ 2) ^ S n) at 1. rewrite <- (Rplus_0_r ((/ 2) ^ S n)). apply Rplus_le_compat_l. apply pow_le; apply Rle_0_inv_2. apply Rplus_le_compat_l. rewrite Rplus_0_r; apply Rle_refl. apply Rplus_le_compat_l. rewrite Rplus_0_l; apply pow_le; apply Rle_0_inv_2. repeat rewrite Rplus_0_r; apply Rle_refl. Qed.
imports: Reals Lia Lra