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 le_max_active_size proof_tree p :
In p (activations proof_tree) -> term_size (proj_left p) + value_size (proj_right p) <= max_active_size proof_tree.