proposition: Lemma ncvg_lt (u : nat -> R) (l1 l2 : \bar R) : (l1 < l2)%E -> ncvg u l1 -> exists K, forall n, (K <= n)%N -> ((u n)%:E < l2)%E.
proof: Proof. move=> lt_12 cv_u_l1; case: (@ncvg_gt (- u) (-l2) (-l1)). by rewrite lte_opp2. by apply/ncvgN. by move=> K cv; exists K => n /cv; rewrite (@lte_opp2 _ _ (u n)%:E). Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.bigenough.bigenough mathcomp.classical(boolp classical_sets functions) mathcomp.classical(mathcomp_extra) xfinmap ereal reals discrete topology