Proposition enriched_functor_hom_comp_comm (x : C₁) : enriched_functor_hom_comp · enriched_functor_hom_pr EF EH x = (enriched_functor_hom_pr EG EH x #⊗ enriched_functor_hom_pr EF EG x) · enriched_comp E₂ (F x) (G x) (H x). Proof. unfold enriched_functor_hom_comp. rewrite mor_to_enriched_functor_hom_pr. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.HomFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.OppositeEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Import MonoidalNotations. Section EnrichmentFromArr. End EnrichmentFromArr.