Lemma chain_union_rel_isTotalOrder {X : hSet} {I : UU} {S : I → WOSubset X} (chain : is_wosubset_chain S) : isTotalOrder (chain_union_rel chain). Proof. repeat split. - apply chain_union_rel_istrans. - apply chain_union_rel_isrefl. - apply chain_union_rel_isantisymm. - apply chain_union_rel_istotal. Defined.
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.