Definition lax_slice_invertible_2cell_weq_disp_adj_equiv (HB_2_1 : is_univalent_2_1 B) {c : B} (t₁ t₂ : lax_slice_disp_bicat c) : invertible_2cell t₁ t₂ ≃ disp_adjoint_equivalence (internal_adjoint_equivalence_identity c) t₁ t₂. Proof. use make_weq. - exact lax_slice_invertible_2cell_to_disp_adj_equiv. - use isweq_iso. + exact lax_slice_disp_adj_equiv_to_invertible_2cell. + abstract (intros α ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; cbn ; rewrite vassocl ; rewrite linvunitor_lunitor ; apply id2_right). + abstract (intros α ; use subtypePath ; [ intro ; use isaprop_disp_left_adjoint_equivalence ; [ exact HB_2_1 | apply lax_slice_disp_univalent_2_1 ] | ] ; cbn ; rewrite vassocl ; rewrite lunitor_linvunitor ; apply id2_right). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.