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

Lemma right_from_activation_or_from_left_path lp c1 c2 : andl (map wf lp) -> cache_path c1 c2 lp = true -> maxl (map (fun tv : term * value => value_size (snd tv)) c2) <= max (maxl (map max_active_size lp)) (maxl (map (fun tv : term * value => value_size (snd tv)) c1)).