Definition conservative_1cell_reflect_iso {B : bicat} {a b : B} {f : a --> b} (Hf : conservative_1cell f) {x : B} {g₁ g₂ : x --> a} (α : g₁ ==> g₂) (Hα : is_invertible_2cell (α ▹ f)) : is_invertible_2cell α := Hf x g₁ g₂ α Hα.
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.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.FullyFaithful.