Proposition is_univalent_enriched_relation_twosided_disp_cat : is_univalent_twosided_disp_cat enriched_relation_twosided_disp_cat. Proof. intros X₁ X₂ Y₁ Y₂ p q R₁ R₂. induction p, q ; cbn. use isweqimplimpl. - intro p. use funextsec ; intro x. use funextsec ; intro y. use (isotoid _ (is_univalent_quantale_cosmos V)). use make_z_iso. + exact (pr1 p x y). + exact (pr12 p x y). + split. * apply is_poset_category_quantale_cosmos. * apply is_poset_category_quantale_cosmos. - apply isaset_enriched_relation. - use isaproptotal2. + intro. apply isaprop_is_iso_twosided_disp. + intros. apply isaprop_enriched_relation_square. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.PosetCat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichedRelation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Import MonoidalNotations.