∀ (V : Type u_2) [inst : CategoryTheory.ReflQuiver V] (X : V),
  (CategoryTheory.Cat.FreeRefl.quotientFunctor V).map (CategoryTheory.ReflQuiver.id X).toPath =
    CategoryTheory.CategoryStruct.id ((CategoryTheory.Cat.FreeRefl.quotientFunctor V).obj X)