Definition FinSigFun : (∑ n : nat, unit ⨿ (stn n ⨿ unit)) → list nat. Proof. induction 1 as [n p]. induction p as [_|p]. - apply []. - induction p as [p|]. + apply (FinSigConstructors _ p). + apply (FinSigElim n). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Sets. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.SubstitutionSystems.BindingSigToMonad. Require Import UniMath.SubstitutionSystems.LiftingInitial_alt.