Proposition internal_postcomp_comp (x : V) {y₁ y₂ y₃ : V} (g₁ : y₁ --> y₂) (g₂ : y₂ --> y₃) : internal_postcomp x (g₁ · g₂) = internal_postcomp x g₁ · internal_postcomp x g₂. Proof. use internal_funext. intros a h. rewrite tensor_split. rewrite tensor_comp_r_id_r. rewrite !assoc'. unfold internal_postcomp. rewrite !internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. apply maponpaths. rewrite !assoc. rewrite internal_beta. 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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.