Definition universalMapUniqueness' {C:category} {X:[C^op,HSET]} {r:Representation X} {c:C} (x : c ⇒ X) (f : c --> universalObject r) : f = r \\ x -> r ⟲ f = x := pathsweq1' (universalProperty r c) f x.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import Require Import Require Import UniMath.MoreFoundations.Tactics.