proposition: Lemma z_iso_Equalizer_of_same_map {y z : C} {f g : y --> z} (E : Equalizer f g) (p:f = g) : is_z_isomorphism (EqualizerArrow E).
proof: Proof. induction p. use (make_is_z_isomorphism _ (from_Equalizer_to_Equalizer (identity_asEqualizer f) E)). use z_iso_from_Equalizer_to_Equalizer_inverses. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Retracts