Definition activation_function (function_default : function) (p: cbv) :=
  match p with
    | cbv_update _ _ _ _ (fapply f _) _ _ => f
    | _                                   => function_default
  end.

Lemma activations_trans p p' p'' : wf p'' -> In p (activations p') -> In p' (activations p'') -> In p (activations p'').