Fixpoint FA_path p p' (lp : list cbv) := match lp with
| [] => p = p'
| h :: t => In p (first_activations h) /\ FA_path h p' t
end.

Lemma length_fapplies_le_functions s t : length (fapplies_in_term (@subst variable function constructor s t)) <= length (functions_of_term t).