Definition iso_projects_from_CONE (a b : CONE) (f : z_iso a b) : is_z_isomorphism (ConeConnect (pr1 f)). Proof. set (T:=z_iso_inv_after_z_iso f). set (T':=z_iso_after_z_iso_inv f). exists (ConeConnect (inv_from_z_iso f)). split; simpl. - apply (base_paths _ _ T). - apply (base_paths _ _ T'). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors.