Lemma SignatureMor_eq (Ht Ht' : Signature C D D') (f g : SignatureMor Ht Ht') : (pr1 f: pr1 Ht ⟹ pr1 Ht') = (pr1 g: pr1 Ht ⟹ pr1 Ht') -> f = g. Proof. intros H. apply subtypePath; trivial. now intros α; repeat (apply impred; intro); apply functor_category_has_homsets. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. 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.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PointedFunctorsComposition. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.SubstitutionSystems.Notation. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.SubstitutionSystems.BinProductOfSignatures. Require Import UniMath.SubstitutionSystems.SumOfSignatures.