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)).