proposition: Lemma comult_before_inner_swap_and_swap (mx my : comonoid M) : δ_{mx} #⊗ δ_{my} · (inner_swap M _ _ _ _ · sym_mon_braiding M _ _ #⊗ sym_mon_braiding M _ _) = δ_{mx} #⊗ δ_{my} · (sym_mon_braiding M (_ ⊗ _) (_ ⊗ _) · inner_swap M _ _ _ _).
proof: Proof. apply maponpaths. apply inner_swap_commute_with_swap. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Examples.Sigma UniMath.CategoryTheory.Monoidal.Examples.Fullsub UniMath.CategoryTheory.Monoidal.Examples.DiagonalFunctor UniMath.CategoryTheory.Monoidal.Examples.ConstantFunctor UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Categories.Dialgebras