Definition Y_iscontr (b b' : D) (f : b --> b') : iscontr (Y f). Proof. assert (HH : isaprop (iscontr (Y f))). { apply isapropiscontr. } apply (pr1 wH b (tpair (λ x, isaprop x) (iscontr (Y f)) HH)). intros [a0 h0]. apply (pr1 wH b' (tpair (λ x, isaprop x) (iscontr (Y f)) HH)). intros [a0' h0']. exists (Y_inhab b b' f a0 h0 a0' h0'). apply Y_contr_eq. 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.