Definition wosub_le_smaller {X:hSet} (S T:WOSubset X) : hProp := (S ≼ T) ∧ (∃ t:T, t ∉ S).
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.