proposition: Lemma weqpathsinpr_quot_functor X x y : hequiv X x y ≃ pr_quot_functor X x = pr_quot_functor X y.
proof: Proof. apply (weqpathsinsetquot (hequiv X)). 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