Proposition is_univalent_graph_enriched_profunctor_twosided_disp_cat : is_univalent_twosided_disp_cat graph_enriched_profunctor_twosided_disp_cat. Proof. intros x x' y y' p q f g. induction p, q ; cbn in *. use isweqimplimpl. - intros h. pose (p := pr1 h) ; cbn in p. rewrite lmap_e_arr_id, rmap_e_arr_id in p. rewrite !id_right in p. exact (!p). - apply homset_property. - use isaproptotal2. + intro. apply isaprop_is_iso_twosided_disp. + intro ; intros. apply isaprop_graph_enriched_profunctor_disp_mor. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorSquares. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.StandardProfunctors. 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. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Import MonoidalNotations.