Definition disp_adjequiv_sigma_help (x : C) (xx1 : D₁ x) (xx2 yy2 : D₂ (x,, xx1)) : disp_adjoint_equivalence (@internal_adjoint_equivalence_identity (total_bicat D₁) (x,, xx1)) xx2 yy2 → disp_adjoint_equivalence (invmap (adjoint_equivalence_total_disp_weq xx1 xx1) ((internal_adjoint_equivalence_identity x) ,,disp_identity_adjoint_equivalence xx1)) xx2 yy2. Proof. intros p. simple refine (pr1 p ,, ((pr112 p ,, (pr1 (pr212 p) ,, pr2 (pr212 p))) ,, _ ,, (_ ,, _))). - abstract (apply help_disp_left_adjoint_axioms ; apply HD₂). - abstract (apply LG₂). - abstract (apply LG₂). 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.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.