Definition param_distr_pentagon_eq_body_RHS (v w : Mon_V) (dv: [A, A'] ⟦ param_distributivity_dom v, param_distributivity_codom v ⟧) (dw: [A, A'] ⟦ param_distributivity_dom w, param_distributivity_codom w ⟧) : [A, A'] ⟦ precompF (monoidal_functor_map_dom Mon_V Mon_EndA' FA' (v,, w)), postcompF (monoidal_functor_map_codom Mon_V Mon_EndA FA (v,, w))⟧. Proof. set (aux1 := # (post_comp_functor (FA' w)) dv). set (aux2 := # (pre_comp_functor (FA v)) dw). set (aux3 := # postcompF (lax_monoidal_functor_μ FA (v,,w))). set (auxr := aux1 · aux2). exact (auxr · aux3). Defined.
Require Import UniMath.Foundations.PartD. 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Import MonoidalNotations. Import BifunctorNotations. Import MonoidalNotations.