Definition inner_swap''' (x y z w : V) : V⟦(x ⊗ y) ⊗ (z ⊗ w), (x ⊗ z) ⊗ (y ⊗ w)⟧. Proof. refine (sym_mon_braiding _ _ _ ⊗^{V}_{r} _ · mon_lassociator _ _ _ · sym_mon_braiding _ _ (_ ⊗ _) · _). refine (_ · _ ⊗^{V}_{l} sym_mon_braiding _ _ _). refine (_ · mon_rassociator _ _ _). refine (_ · x ⊗^{V}_{l} mon_lassociator _ _ _). apply mon_lassociator. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.