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