Fixpoint activations (proof_tree : cbv) : list cbv :=
match proof_tree with
| cbv_constr lp _ _ => flat_map activations lp
| cbv_split lp p _ _ => activations p ++ flat_map activations lp
| cbv_function _ _ p _ _ as p' => p' :: activations p
end.

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