Definition is_lim_seq (u : nat -> NonnegativeReals) (l : NonnegativeReals) : hProp := make_hProp (∏ eps : NonnegativeReals, 0 < eps -> hexists (λ N : nat, ∏ n : nat, N ≤ n -> u n < l + eps × l < u n + eps)) (impred_isaprop _ (λ _, isapropimpl _ _ (pr2 _))).
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.