Corollary activations_inCBV: forall p pi:cbv,
   In p (activations pi) -> InCBV p pi.Definition functions_of_prog : list function :=
  map (fun x => match x with | rule_intro f _ _ => f end) prog.

Lemma activations_wf : forall proof_tree p, wf proof_tree -> In p (activations proof_tree) -> wf p.