Definition proper_subtypes_set (X:UU) : hSet := ∑ S : subtype_set X, hProp_to_hSet (∃ x, ¬ (S x)).
Require Import UniMath.MoreFoundations.DecidablePropositions. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.OrderTheory.OrderedSets.OrderedSets.