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(*             Bornes globales                                                     *)
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(* Lemma 69 *)
Lemma QI_never_increase_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 ->
term_assignment qic qif (proj_left pi) <= term_assignment qic qif (proj_left proof_tree).