Proposition change_of_base_postcomp {x y : C} (w : C) (f : x --> y) : postcomp_arr change_of_base_enrichment w f = #F (postcomp_arr E w f). Proof. unfold postcomp_arr ; cbn. rewrite !functor_comp. rewrite !assoc. apply maponpaths_2. rewrite mon_functor_linvunitor. rewrite !assoc'. apply maponpaths. rewrite <- tensor_mon_functor_tensor. rewrite functor_id. rewrite !assoc. rewrite <- tensor_comp_id_r. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Import MonoidalNotations.