Lemma functor_id_id (A B : precategory) (G : functor A B) (a : A) (f : a --> a) : f = identity _ -> #G f = identity _ . Proof. intro e. intermediate_path (#G (identity a )). - apply maponpaths. apply e. - apply functor_id. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence.