proposition: Lemma id_functor_cat : forall a b x, Category.axioms a -> Category.axioms b -> ob (functor_cat a b) x -> id (functor_cat a b) x = vident x.
proof: Proof. ir. uf functor_cat; rw id_create. tv. rw inc_functor_set. wrr ob_functor_cat. Qed.
imports: Arith nat_trans