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

Lemma nb_judgements_sub_bound i s p c1 t c2 v : wf (cbv_update i s p c1 t c2 v) -> nb_judgements_sub (cbv_update i s p c1 t c2 v) <= activation_bound prog (term_size t).