Definition four_rec {A : UU} (a b c d : A) : stn 4 -> A. Proof. induction 1 as [n p]. induction n as [|n _]; [apply a|]. induction n as [|n _]; [apply b|]. induction n as [|n _]; [apply c|]. induction n as [|n _]; [apply d|]. induction (nopathsfalsetotrue p). 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.