proposition: Lemma phi (a0 : C) : pr1 (pr1 (functor_composite H GG)) a0 = pr1 (pr1 F) a0.
proof: Proof. exact (!Xphi _ (XtripleF a0)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.precomp_fully_faithful UniMath.CategoryTheory.DaggerCategories.Categories UniMath.CategoryTheory.DaggerCategories.Functors UniMath.CategoryTheory.DaggerCategories.Transformations UniMath.CategoryTheory.DaggerCategories.Unitary UniMath.CategoryTheory.DaggerCategories.Univalence UniMath.CategoryTheory.DaggerCategories.FunctorCategory UniMath.CategoryTheory.DaggerCategories.Functors.FullyFaithful UniMath.CategoryTheory.DaggerCategories.Functors.WeakEquivalences