Definition fully_faithful_1cell_faithful {B : bicat} {a b : B} {f : a --> b} (Hf : fully_faithful_1cell f) : faithful_1cell f := pr1 Hf.
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.