proposition: Lemma ub_lt_2_pos : forall x ub lb, lb < x -> x < ub -> 0 < (ub-lb)/2.
proof: Proof. intros x ub lb lb_lt_x x_lt_ub. assert (T : 0 < ub - lb). lra. unfold Rdiv ; apply Rlt_mult_inv_pos ; intuition (auto with real). Qed.
imports: Reals RFsequence Lra PeanoNat