Proposition mor_to_enriched_functor_hom_pr {v : V} (fv : ∏ (i : C₁) , v --> E₂ ⦃ F i, G i ⦄) (p : ∏ (x y : C₁), fv x · σ x y = fv y · ρ x y) (i : C₁) : mor_to_enriched_functor_hom fv p · enriched_functor_hom_pr i = fv i. Proof. unfold mor_to_enriched_functor_hom, enriched_functor_hom_pr. rewrite !assoc. rewrite EqualizerCommutes. apply (ProductPrCommutes _ _ _ P₁). 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.