proposition: Lemma modulus_h_productive_h: forall mu alpha (h:emits_h mu alpha), let mu':=fstT (sndT (modulus_h mu alpha h)) in let alpha':=sndT (sndT (modulus_h mu alpha h)) in productive_h mu alpha -> productive_h mu' alpha'.
proof: Proof. intros mu alpha h mu' alpha' h_p_alpha. constructor. intro n. inversion h_p_alpha. generalize (H (S n)). subst mu'. subst alpha'. apply step_productive_h_S_inv_2. Defined.
imports: digits