Definition Church_gen_body (n : nat) (ξ : sortToSet) : UntypedForest_gen_ctx_sort (ctx_ext (ctx_ext ξ sv) sv) st. Proof. induction n. - simple refine (pr1 (pr1 UntypedForest_eta_gen _) _ _). cbn. apply ii1. exists (idpath _). exact tt. - refine (pr1 (pr1 (app_map_gen 1) _) _ _). split ; exists (idpath _). + change (UntypedForest_gen_ctx_sort (ctx_ext (ctx_ext ξ sv) sv) sv). simple refine (pr1 (pr1 UntypedForest_eta_gen _) _ _). cbn. apply ii2. apply ii1. exists (idpath _). exact tt. + exact IHn. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.PartB. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. 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.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.CategoryTheory.Core.Isos. 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.