Lemma Forest_eta_gen_natural'_pointwise (ξ ξ' : sortToSet) (f : sortToSet ⟦ ξ, ξ' ⟧) (u : sort) : pr1 f u · pr1 (pr1 Forest_eta_gen ξ') u = pr1 (pr1 Forest_eta_gen ξ) u · pr1 (# (pr1 Forest_gen) f) u. Proof. apply (nat_trans_eq_weq HSET _ _ (Forest_eta_gen_natural' ξ ξ' f)). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartB. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.FunctorCoalgebras. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Chains.Chains. Require Import UniMath.CategoryTheory.Chains.Cochains. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.SubstitutionSystems.SigmaMonoids. Require Import UniMath.SubstitutionSystems.MultiSortedBindingSig. Require Import UniMath.SubstitutionSystems.MultiSorted_alt. Require Import UniMath.SubstitutionSystems.MultiSorted_actegorical. Require Import UniMath.SubstitutionSystems.MultiSortedMonadConstruction_actegorical. Require Import UniMath.SubstitutionSystems.MultiSortedMonadConstruction_coind_actegorical. Require Import UniMath.SubstitutionSystems.ContinuitySignature.InstantiateHSET. Require Import UniMath.SubstitutionSystems.MultiSortedEmbeddingIndCoindHSET. Require Import UniMath.SubstitutionSystems.SortIndexing.