Lemma FiveLemma {FR1 FR2 : FiveRow} (FRM : FiveRowMorphism FR1 FR2) (H1 : is_z_isomorphism (FMor1 FRM)) (H2 : is_z_isomorphism (FMor2 FRM)) (H4 : is_z_isomorphism (FMor4 FRM)) (H5 : is_z_isomorphism (FMor5 FRM)) : is_z_isomorphism (FMor3 (A:=A) FRM). Proof. use monic_epi_is_iso. - use FiveLemma_isMonic. + exact H1. + exact H2. + exact H4. + exact H5. - use FiveLemma_isEpi. + exact H1. + exact H2. + exact H4. + exact H5. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Opp. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Morphisms. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.AbelianToAdditive. Require Import UniMath.CategoryTheory.AbelianPushoutPullback. Require Import UniMath.CategoryTheory.ShortExactSequences. Require Import UniMath.CategoryTheory.PseudoElements. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.BinDirectSums.