Definition bicat_adjoint_equivalence_is_fullsub_adjoint_equivalence (X Y : fullsubbicat) : @adjoint_equivalence C (pr1 X) (pr1 Y) ≃ adjoint_equivalence X Y. Proof. apply invweq. use weqtotal2. - apply invweq. apply weqtodirprodwithunit. - intro ; cbn. apply fullsub_left_adjoint_equivalence_is_bicat_left_adjoint_equivalence. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. 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. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.