proposition: Lemma AbelianPullbackEpiisPushout2 {x y z : A} (f : x --> z) (g : Epi A y z) (Pb : Pullback f g) : isPushout (PullbackPr1 Pb) (PullbackPr2 Pb) f g (PullbackSqrCommutes Pb).
proof: Proof. set (Pb' := make_Pullback _ (is_symmetric_isPullback _ (isPullback_Pullback Pb))). use is_symmetric_isPushout. - exact (! (PullbackSqrCommutes _ )). - exact (AbelianPullbackEpiisPushout1 g f Pb'). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets 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.opp_precat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.AbelianToAdditive UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinDirectSums