Definition all_is_invertible_is_is_invertible_2cell {F G : ps_base} {η ε : F --> G} (α : η ==> ε) : (∏ (X : C), is_invertible_2cell (α X)) ≃ is_invertible_2cell α. Proof. use weqimplimpl. - exact (all_is_invertible_to_is_invertible_2cell α). - exact (is_invertible_2cell_to_all_is_invertible α). - apply impred ; intro. apply isaprop_is_invertible_2cell. - apply isaprop_is_invertible_2cell. 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.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.AdjointUnique.