proposition: Lemma is_univalent_disp_algebraic_theory_data_disp_cat : is_univalent_disp algebraic_theory_data_disp_cat.
proof: Proof. apply is_univalent_disp_iff_fibers_are_univalent. intros T Tdata Tdata'. use isweq_iso. - intro f. apply pathsdirprod; repeat (apply funextsec; intro); apply (pr1 f). - intro. apply isasetdirprod; repeat (apply impred_isaset; intro); apply setproperty. - intro. apply z_iso_eq. apply subtypePath. { intro. do 4 (apply impred_isaprop; intro). apply setproperty. } do 2 (apply funextsec; intro). apply setproperty. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Limits UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.AlgebraicTheories.IndexedSetCategory UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms