Definition SumBindingSig : BindingSig -> BindingSig -> BindingSig. Proof. intros s1 s2. use tpair. - apply (BindingSigIndex s1 ⨿ BindingSigIndex s2). - use tpair. + apply (isasetcoprod _ _ (BindingSigIsaset s1) (BindingSigIsaset s2)). + induction 1 as [i|i]; [ apply (BindingSigMap s1 i) | apply (BindingSigMap s2 i) ]. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Chains.All. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Categories.HSET.Colimits. Require Import UniMath.CategoryTheory.Categories.HSET.Structures. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.SignatureExamples. Require Import UniMath.SubstitutionSystems.SumOfSignatures. Require Import UniMath.SubstitutionSystems.BinProductOfSignatures. Require Import UniMath.SubstitutionSystems.SubstitutionSystems. Require Import UniMath.SubstitutionSystems.LiftingInitial_alt. Require Import UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems. Require Import UniMath.SubstitutionSystems.Notation.