Definition cocone_paths {C : category} {g : graph} {d : diagram g C} {x : C} (cc1 cc2 : cocone d x) (eqin : ∏ g, coconeIn cc1 g = coconeIn cc2 g): cc1 = cc2. Proof. use subtypePath'. - apply funextsec. exact eqin. - repeat (apply impred_isaprop; intro). apply C. 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.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core.