proposition: Lemma ap_a_path_object x y Ha Hb Hf : ap (@a) (@path_object x y Ha Hb Hf) = Ha.
proof: Proof. destruct x, y; simpl in *. destruct Ha, Hb, Hf; simpl in *. reflexivity. Qed.
imports: Category.Core Functor.Core NaturalTransformation.Core Functor.Composition.Core NaturalTransformation.Paths NaturalTransformation.Composition.Core Category.Morphisms FunctorCategory.Core Pseudofunctor.Core NaturalTransformation.Composition.Laws Trunc Types.Sigma Basics.Tactics