proposition: Lemma functional_2_is_monoid_action : is_monoid_action functional_2_monoid_action_data.
proof: Proof. split. - intro x. apply functional_2_eq. simpl. apply (maponpaths pr1 (runax lambda_algebra_monoid (_ ,, is_functional_2_to_is_functional_1 _ (pr2 x))) ). - intros. apply functional_2_eq. exact (!compose_assoc _ _ _). Qed.
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