proposition: Lemma elements_id_comp : disp_cat_id_comp HSET elements_ob_mor.
proof: Proof. apply tpair; simpl. - intros X x. apply idpath. - intros X Y Z f g x y z e_fx_y e_gy_z. cbn. eapply pathscomp0. apply maponpaths, e_fx_y. apply e_gy_z. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Limits UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing UniMath.CategoryTheory.DisplayedCats.Examples.Sigma