Definition iso_to_Terminal {C : category} (T : Terminal C) (x : C) (i : z_iso T x) : isTerminal C x. Proof. intros w. use iscontraprop1. - abstract (use invproofirrelevance ; intros φ₁ φ₂ ; refine (!(id_right _) @ _ @ id_right _) ; rewrite <- !(z_iso_after_z_iso_inv i) ; rewrite !assoc ; apply maponpaths_2 ; apply TerminalArrowEq). - exact (TerminalArrow T w · i). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Monics.