Proposition eq_graph_enriched_profunctor_mor {xyf₁ xyf₂ : graph_enriched_profunctor_ob} {f g : graph_enriched_profunctor_mor xyf₁ xyf₂} (r₁ : graph_enriched_profunctor_mor_pr1 f = graph_enriched_profunctor_mor_pr1 g) (r₂ : graph_enriched_profunctor_mor_pr2 f = graph_enriched_profunctor_mor_pr2 g) : f = g. Proof. induction f as [ f₁ [ f₂ p ]]. induction g as [ g₁ [ g₂ q ]]. cbn in *. induction r₁, r₂ ; cbn. do 2 apply maponpaths. apply homset_property. 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.