proposition: Lemma inner_swap_characterization12 (x y z w : V) : inner_swap' x y z w = inner_swap'' x y z w.
proof: Proof. unfold inner_swap', inner_swap''. apply maponpaths. rewrite ! (bifunctor_leftcomp V). rewrite ! assoc'. do 2 apply maponpaths. apply monoidal_associatorinvnatleft. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric