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

Lemma nb_nodes_bound_gen 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_nodes p <= A * (1 + activation_bound prog S).