proposition: Lemma pushout_to_epi : isPushout f f (identity _) (identity _) (idpath _) -> isEpi f.
proof: Proof. intros hf. intros D p1 p2 hp. apply hf in hp. destruct hp as [[p [hp1 hp2]] _]. now rewrite <- hp1,hp2. Qed.
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