Definition is_invertible_2cell_to_all_is_invertible {F G : ps_base} {η ε : F --> G} (α : η ==> ε) : is_invertible_2cell α → (∏ (X : C), is_invertible_2cell (α X)). Proof. intros Hα X. use tpair. - exact (Hα^-1 X). - split ; cbn. + exact (maponpaths (λ φ, φ X) (vcomp_rinv Hα)). + exact (maponpaths (λ φ, φ X) (vcomp_linv Hα)). 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.