Lemma inner_swap_characterization23 (x y z w : V) : inner_swap'' x y z w = inner_swap''' x y z w. Proof. unfold inner_swap'', inner_swap'''. rewrite ! assoc. do 2 apply maponpaths_2. rewrite ! (bifunctor_leftcomp V). rewrite ! assoc. apply maponpaths_2. apply sym_mon_tensor_lassociator1. Qed.
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.