proposition: Proposition internal_eval_pair (x y : V) : internal_pair (x ⊸ y) x · internal_lam (internal_eval _ _ · internal_eval _ _) = identity (x ⊸ y).
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric