proposition: Lemma ShortExactFiveLemma {SSE1 SSE2 : ShortExact A} (Mor : MPMor SSE1 SSE2) (H2 : is_z_isomorphism (MPMor1 Mor)) (H4 : is_z_isomorphism (MPMor3 Mor)) : is_z_isomorphism (MPMor2 Mor).
proof: Proof. set (FR1 := ShortExactRow1 Mor). set (FR2 := ShortExactRow2 Mor). set (FM := ShortExactMor Mor). use (FiveLemma FM). - exact (is_z_isomorphism_identity _). - exact H2. - exact H4. - exact (is_z_isomorphism_identity _). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.AbelianToAdditive UniMath.CategoryTheory.AbelianPushoutPullback UniMath.CategoryTheory.ShortExactSequences UniMath.CategoryTheory.PseudoElements UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinDirectSums