Definition ps_base_is_univalent_2_0 (HD : is_univalent_2 D) : is_univalent_2_0 ps_base. Proof. intros F G. use weqhomot. - simple refine (adjequiv_ps_base_weq F G ∘ _)%weq. simple refine (_ ∘ make_weq _ (isweqtoforallpaths _ _ _))%weq. simple refine (weqonsecfibers _ _ _). intro X ; cbn. exact (make_weq (idtoiso_2_0 (F X) (G X)) (pr1 HD _ _)). - intros p. induction p. use subtypePath. { intro. apply isaprop_left_adjoint_equivalence. exact (ps_base_is_univalent_2_1 (pr2 HD)). } reflexivity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique.