Definition X_aux_type_center_of_contr (b : D) (anot : C)(hnot : unitary dagD (H anot) b) : X b. Proof. set (cnot := F anot). use tpair. - exists cnot. intros c u. unfold cnot. set (u' := fully_faithful_reflects_unitary dagH fH c anot (unitary_comp u (unitary_inv hnot))). exact (dagger_functor_on_unitary dagF _ _ u'). - exact (λ t t' f p, X_aux_type_center_of_contr_proof b anot hnot t t' f p). Defined.
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.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts. Require Import UniMath.CategoryTheory.precomp_fully_faithful. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.FunctorCategory. Require Import UniMath.CategoryTheory.DaggerCategories.Functors.FullyFaithful. Require Import UniMath.CategoryTheory.DaggerCategories.Functors.WeakEquivalences.