Lemma is_univalent_pregroupoid_is_univalent {pgpd : groupoid} : is_univalent_pregroupoid pgpd -> is_univalent pgpd. Proof. intros ig. intros a b. use (isofhlevelff 0 idtoiso (morphism_from_z_iso _ _)). + use (isweqhomot (idtomor _ _)). * intro p; destruct p; reflexivity. * apply ig. + apply (morphism_from_iso_is_incl pgpd). Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat.