Proposition pairing_rassociator {a x y z : C} (f : a --> x) (g : a --> y) (h : a --> z) : ⟨f,⟨g,h⟩⟩ · mon_rassociator _ _ _ = ⟨⟨f,g⟩,h⟩. Proof. rewrite <- pairing_lassociator. rewrite !assoc'. rewrite mon_lassociator_rassociator. rewrite id_right. apply idpath. 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.