Definition is_equiv_over_id_to_is_equiv_over : is_equiv_over F L. Proof. simple refine (((R ,, (η ,, ε)) ,, _ ,, _) ,, _ ,, _). - abstract (intros x xx ; cbn ; refine (pr121 FF x xx @ _) ; apply maponpaths_2 ; apply homset_property). - abstract (intros x xx ; cbn ; refine (pr221 FF x xx @ _) ; apply maponpaths_2 ; apply homset_property). - intros x xx. apply FF. - intros x xx. apply FF. Defined.
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.