Lemma PushoutArrow_PushoutIn1 {a b c : C} {f : C⟦a, b⟧} {g : C⟦a, c⟧} (Po : Pushout f g) (e : C) (h : C⟦b , e⟧) (k : C⟦c, e⟧) (H : f · h = g · k) : PushoutIn1 Po · PushoutArrow Po e h k H = h. Proof. exact (colimArrowCommutes Po e _ Two). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Pushouts.