Definition disp_left_adjoint_equivalence_over_id_weq_lift : disp_left_adjoint_equivalence (internal_adjoint_equivalence_identity (pr1 x)) ff ≃ disp_left_adjoint_equivalence (internal_adjoint_equivalence_identity x) ff. Proof. use weq_iso. - exact to_disp_left_adjoint_equivalence_over_id_lift. - exact from_disp_left_adjoint_equivalence_over_id_lift. - exact disp_left_adjoint_equivalence_over_id_weq_lift_left. - exact disp_left_adjoint_equivalence_over_id_weq_lift_right. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Section FromLift. End FromLift.