proposition: Lemma univ_surj_nt_unique : ∏ g (H : nat_trans_comp _ _ _ p g = f) b, g b = univ_surj_nt b.
proof: Proof. intros g hg b. apply nat_trans_eq_pointwise. unfold univ_surj_nt. set (coeq := make_Coequalizer _ _ _ _ _). use (isCoequalizerOutUnique _ _ _ _ (isCoequalizer_Coequalizer coeq)). apply hg. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Epis UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.EpiFacts UniMath.CategoryTheory.Limits.Coequalizers