Proposition internal_eval_pair (x y : V) : internal_pair (x ⊸ y) x · internal_lam (internal_eval _ _ · internal_eval _ _) = identity (x ⊸ y). Proof. use internal_funext. intros a h. rewrite tensor_comp_r_id_r. rewrite !assoc'. rewrite internal_beta. etrans. { rewrite !assoc. apply maponpaths_2. rewrite tensor_split. rewrite !assoc'. unfold internal_pair. rewrite internal_beta. apply id_right. } 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.