Definition X_aux_type_center_of_contr (b : B) (anot : A)(hnot : z_iso (H anot) b) : X b. Proof. set (cnot := F anot). set (g := fun (a : A)(h : z_iso (H a) b) => (fH^-i (z_iso_comp h (z_iso_inv_from_z_iso hnot)))). set (knot := fun (a : A)(h : z_iso (H a) b) => functor_on_z_iso F (g a h)). simpl in *. exists (tpair _ (F anot) knot). simpl. apply X_aux_type_center_of_contr_proof. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.