proposition: Lemma EpiPushoutisEpi {a b c : C} (E : Epi _ a b) (g : a --> c) (PB : Pushout E g) : isEpi (PushoutIn2 PB).
proof: Proof. apply make_isEpi. intros z g0 h X. use (MorphismsOutofPushoutEqual (isPushout_Pushout PB) _ _ _ X). set (X0 := maponpaths (λ f, g · f) X); simpl in X0. rewrite assoc in X0. rewrite assoc in X0. rewrite <- (PushoutSqrCommutes PB) in X0. rewrite <- assoc in X0. rewrite <- assoc in X0. apply (pr2 E _ _ _) in X0. apply X0. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Core.Functors