Definition WOSubset_plus_point {X:hSet} (S:WOSubset X) (z:X) (nSz : ¬ S z) : LEM -> WOSubset X := λ lem, subtype_plus S z,, TOSrel (TOSubset_plus_point S z nSz),, TOtotal (TOSubset_plus_point S z nSz),, hasSmallest_WOSubset_plus_point S z nSz lem.
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.