Lemma inv_from_z_iso_z_iso_from_Pushout (a b c : C) (f : a --> b) (g : a --> c) (Pb : Pushout f g) (Pb' : Pushout f g): inv_from_z_iso (z_iso_from_Pushout_to_Pushout Pb Pb') = from_Pushout_to_Pushout Pb' Pb. Proof. apply pathsinv0. apply inv_z_iso_unique'. set (T:= are_inverses_from_Pushout_to_Pushout Pb' Pb). apply (pr1 T). 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.