Definition Cauchy_seq (u : nat → hr_ConstructiveField) : hProp. Proof. apply (make_hProp (∏ c : NonnegativeReals, 0 < c -> ∃ N : nat, ∏ n m : nat, N ≤ n -> N ≤ m -> hr_abs (u m - u n)%ring < c)). apply impred_isaprop ; intro. apply isapropimpl. apply pr2. Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.