(***********************************************************************************)
(*                                                                                 *)
(*             Bornes globales                                                     *)
(*                                                                                 *)
(***********************************************************************************)

Lemma cache_left_bounded_global qic qif cs: forall pi proof_tree:cbv,
valid_QI qic qif cs -> wf proof_tree ->
cache_bounded qic qif (cache_left proof_tree) -> InCBV pi proof_tree ->
cache_bounded qic qif (cache_left pi).