Lemma PushoutArrow_PushoutIn2 {a b c : C} {f : a --> b} {g : a --> c} (Pb : Pushout f g) e (h : b --> e) (k : c --> e) (H : f · h = g · k) : PushoutIn2 Pb · PushoutArrow Pb e h k H = k. Proof. exact (pr2 (pr2 (pr1 (isPushout_Pushout Pb e h k H)))). Qed.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Core.Functors.