Definition cbv_cache_entry (proof_tree : cbv) := (proj_left proof_tree, proj_right proof_tree).

Lemma right_from_activation_or_from_left p : wf p -> maxl (map (fun tv : term * value => value_size (snd tv)) (cache_right p)) <= max (max_active_size p) (maxl (map (fun tv : term * value => value_size (snd tv)) (cache_left p))).