Proposition isaprop_is_equiv_over_id : isaprop (is_equiv_over_id F). Proof. use invproofirrelevance. intros HF₁ HF₂. use subtypePath. { intro. apply isaprop_form_equiv_over_id. } use subtypePath. { intro. apply isaprop_form_disp_adjunction_id. } use (path_right_adjoint_over_id_data HD₁ HD₂). - exact (isaprop_is_equiv_over_id_nat_z_iso HF₁ HF₂). - exact (isaprop_is_equiv_over_id_eq_1 HF₁ HF₂). - exact (isaprop_is_equiv_over_id_eq_2 HF₁ HF₂). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq.