Definition to_equivalence_mnd_help {B : bicat} (HB : is_univalent_2_0 B) {x y : B} (l : adjoint_equivalence x y) {mx : disp_mnd B x} {my : disp_mnd B y} (m₁ := x ,, mx : mnd B) (m₂ := y ,, my : mnd B) (Hl : mx -->[ l ] my) (ml := pr1 l ,, Hl : m₁ --> m₂) (Hγ : is_invertible_2cell (mnd_mor_endo ml)) : left_adjoint_equivalence ml. Proof. revert x y l mx my m₁ m₂ Hl ml Hγ. use (J_2_0 HB). intros x mx mx' m₁ m₂ Hl ml Hγ. use equiv_to_adjequiv. exact (to_equivalence_mnd_help_equiv Hl Hγ). 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.Core.Univalence. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Projection. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap.