Definition all_is_invertible_to_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. intros Hα. use tpair ; cbn in *. - exact (λ x, (Hα x)^-1). - split ; apply funextsec ; intro X ; cbn. + apply vcomp_rinv. + apply vcomp_linv. 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.