Lemma StrengthForSignature_eq (H : [C, D'] ⟶ [C, D] ) (sθ1 sθ2 : StrengthForSignature H) : pr1 sθ1 = pr1 sθ2 -> sθ1 = sθ2. Proof. intro Heq. apply subtypePath; trivial. intro θ. apply isapropdirprod. + apply isaprop_θ_Strength1_int. + apply isaprop_θ_Strength2_int. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PointedFunctors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.SubstitutionSystems.Notation.