proposition: Lemma fun_comp_assoc_and_sym `(F : A ⟶ B) `(G : B ⟶ C) `(H : C ⟶ D) (x : A) : fun_comp_assoc x ∘ fun_comp_assoc_sym x ≈ fmap[H] (fmap[G] (fmap[F] id)).
proof: Proof. simpl; cat. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Functor