Definition Dcuts_Cauchy_seq (u : nat -> Dcuts) : hProp := make_hProp (∏ eps : Dcuts, 0 < eps -> hexists (λ N : nat, ∏ n m : nat, N ≤ n -> N ≤ m -> u n < Dcuts_plus (u m) eps × u m < Dcuts_plus (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.