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