Definition enriched_nat_trans_comp {A B : enriched_precat} {F G H : enriched_functor A B} (a : enriched_nat_trans F G) (b : enriched_nat_trans G H) : enriched_nat_trans F H. Proof. use make_enriched_nat_trans. - intro x. exact (a x · postcompose_underlying_morphism _ (b x)). - abstract (intros x y; rewrite postcompose_underlying_morphism_composite; rewrite assoc; rewrite enriched_nat_trans_ax; rewrite assoc'; rewrite pre_post_compose_commute; rewrite assoc; rewrite enriched_nat_trans_ax; rewrite precompose_underlying_morphism_composite; apply assoc'). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Core.Isos. Import MonoidalNotations.