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

Lemma nb_judgements_bound_gen : forall i s p' c1 t c2 v, let p := cbv_update i s p' c1 t c2 v in let A := length (activations p) in let S := max_active_size p in wf p -> nb_judgements p <= A * activation_bound prog S + A + (Datatypes.S (max_arity * nb_nodes p)).