proposition: Lemma is_univalent_path_pregroupoid (X : UU) (iobj : isofhlevel 3 X) : is_univalent_pregroupoid (path_pregroupoid X iobj).
proof: Proof. split. - intros a b. assert (k : idfun (a = b) ~ idtomor a b). { intro p; destruct p; reflexivity. } apply (isweqhomot _ _ k). apply idisweq. - apply has_homsets_path_pregroupoid; assumption. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Groupoids UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.catiso