proposition: Lemma Precomp_is_unitarily_eso (Euniv : is_univalent_dagger dagE) : is_unitarily_eso (dagger_pre_composition_functor_is_dagger_functor dagH dagE).
proof: Proof. intros [F dagF] p' f. apply f. exists (_ ,, GG_is_dagger_functor dagF Euniv). apply idtodaggeriso. use subtypePath. { intro ; apply isaprop_is_dagger_functor. } apply is_preimage_for_pre_composition. Qed.
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