Proposition enriched_rezk_completion_ump_comm_laws : is_nat_trans G (F ∙ enriched_rezk_completion_ump_functor) (λ x, enriched_rezk_completion_ump_functor_iso (F x) (identity_z_iso (F x))). Proof. intros x y f ; cbn. refine (!_). refine (enriched_rezk_completion_ump_functor_mor_eq _ f _ (identity_z_iso _) _). cbn. rewrite id_right, id_left. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.FullyFaithful. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FunctorCategory. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.Precomposition. Require Import UniMath.CategoryTheory.Monoidal.Categories.