Definition isGlobalBlock {F V : Type} (ge : Genv.t F V) :=
  fun b => (fst (genv2blocksBool ge)) b || (snd (genv2blocksBool ge)) b.

Lemma restrict_preserves_globals: forall {F V} (ge:Genv.t F V) j X (PG : meminj_preserves_globals ge j) (Glob : forall b, isGlobalBlock ge b = true -> X b = true), meminj_preserves_globals ge (restrict j X).