Definition terms_and_indices_from_one_log_ind (net : network) : Prop :=
    terms_and_indices_from_one_log net /\ terms_and_indices_from_one_log_nw net.

Lemma terms_and_indices_from_one_app : forall xs ys, terms_and_indices_from_one xs -> terms_and_indices_from_one ys -> terms_and_indices_from_one (xs ++ ys).