Proposition is_univalent_quantale_enriched_profunctor_twosided_disp_cat : is_univalent_twosided_disp_cat quantale_enriched_profunctor_twosided_disp_cat. Proof. intros C₁ C₂ C₃ C₄ p₁ p₂ P Q. induction p₁, p₂. use isweqimplimpl. - cbn. intro τ. use eq_profunctor_quantale_enrichment. intros y x. use (isotoid _ (is_univalent_quantale_cosmos V)). use make_z_iso. + exact (pr11 τ y x). + exact (pr112 τ y x). + split. * apply is_poset_category_quantale_cosmos. * apply is_poset_category_quantale_cosmos. - apply isaset_profunctor_quantale_enrichment. - use isaproptotal2. + intro. apply isaprop_is_iso_twosided_disp. + intros. apply isaprop_quantale_enriched_profunctor_transformation. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.QuantaleEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.StandardProfunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Invertible. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorSquares. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Coend. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Composition. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.RepresentableLaws. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints. Import MonoidalNotations.