fact: Definition choice_fun (X:hSet) : hSet := ∏ S : proper_subtypes_set X, ∑ x : X, hProp_to_hSet (¬ pr1 S x).
imports: UniMath.MoreFoundations.DecidablePropositions UniMath.MoreFoundations.Propositions UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.AxiomOfChoice UniMath.Combinatorics.OrderedSets