Definition equiv_Initial1 (c : C) : Limits.Initial.Initial C -> Initial. Proof. intros I. use make_Initial. - exact I. - use equiv_isInitial1. exact (pr2 I). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.EqDiag. Require Import UniMath.CategoryTheory.Limits.Initial. Lemma ArrowsFromInitial (I : Initial) (a : C) (f g : C⟦InitialObject I,a⟧) : f = g.