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

Lemma value_size_bounded_by_nb_judgements p :
wf p -> value_size (proj_right p) <= (1 + max (max_active_size p) (maxl (map (fun tv => value_size (snd tv)) (cache_left p)))) * nb_judgements p.