Proposition pairing_tensor {a x y x2 y2 : C} (f : a --> x) (g : a --> y) (f2 : x --> x2) (g2 : y --> y2) : ⟨f,g⟩ · (f2 #⊗ g2) = ⟨f · f2, g · g2⟩. Proof. unfold pairing. rewrite <- assoc, <- tensor_comp_mor. reflexivity. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal. Import MonoidalNotations.