Definition Church_gen_header_sortToSet_data : nat_trans_data (pr1 Church_gen_body_target) (pr1 (functor_compose STLC_gen (projSortToSetvariable (λ s : sort, (s ⇒ s) ⇒ s ⇒ s)))). Proof. intro ξ. use nat_trans_functor_path_pregroupoid. intros s body. exact (Church_gen_header s ξ body). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.Lists. 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.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.