Proposition qi_is_valid : valid_QI mcs qic qif cs.

(* Specifications: *)
Theorem polytime: forall i s p c f lv d v, let t := fapply f lv in let pi := cbv_update i s p c t d v in cbv_wf pi -> cache_bounded qic qif c -> cbv_size pi <= global_bound mcs qif f lv c.
Lemma quote_positive_value p : quote_positive p = quote_value (Npos p).
Theorem plus_polytime: forall i s p c f lv d v, let t := fapply f lv in let pi := cbv_update i s p c t d v in cbv_wf pi -> cache_bounded qic qif c -> cbv_size pi <= global_bound mcs qif f lv c.