Definition cat_with_terminal_disp_cat_left_adjoint_equivalence_help {C₁ C₂ : bicat_of_univ_cats} (F : adjoint_equivalence C₁ C₂) {CC₁ : disp_bicat_cat_with_terminal_disp_cat C₁} {CC₂ : disp_bicat_cat_with_terminal_disp_cat C₂} (FF : CC₁ -->[ pr1 F ] CC₂) (HF₁ := adj_equiv_to_equiv_cat _ F : adj_equivalence_of_cats (pr1 F)) (A := (_ ,, HF₁) : adj_equiv (pr1 C₁) (pr1 C₂)) (HF₂ : is_equiv_over A (pr2 FF)) : left_adjoint_equivalence (B := bicat_cat_with_terminal_disp_cat) (a := (C₁ ,, CC₁)) (b := (C₂ ,, CC₂)) (_ ,, FF).
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.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.StructuredCategories. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats.