Lemma unitary_functors_eq_equiv_unitary_functors_inv_law2 : ∏ y : unitary_functors dagF dagG, unitary_functors_eq_to_unitary_functors (unitary_functors_eq_from_unitary_functors y) = y. Proof. intro. use total2_paths_f. - use (nat_trans_eq (pr2 D)). intro ; apply idpath. - apply funextsec ; intro. apply Isos.isaprop_is_inverse_in_precat. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations.