proposition: Lemma are_inverses_from_Equalizer_to_Equalizer {y z : C} {f g : y --> z} {E E': Equalizer f g} : is_inverse_in_precat (from_Equalizer_to_Equalizer E E') (from_Equalizer_to_Equalizer E' E).
proof: Proof. split; apply pathsinv0; use EqualizerEndo_is_identity; rewrite <- assoc; unfold from_Equalizer_to_Equalizer; repeat rewrite EqualizerCommutes; apply idpath. 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