Ltac address_ordered_auto :=
      auto; repeat match goal with
                   | H: AddressOrdered.eq ?A ?A |- _ => clear H
                   | H: AddressOrdered.eq ?A ?B |- _ => hnf in H; subst A
                   | H: ?A <> ?A |- _ => contradiction H; reflexivity
                   | H: AddressOrdered.lt ?A ?A |- _ =>
                     apply AddressOrdered.lt_not_eq in H; contradiction H; reflexivity
                   | H: AddressOrdered.lt ?A ?B, H': AddressOrdered.lt ?B ?A |- _ =>
                     contradiction (AddressOrdered.lt_not_eq (AddressOrdered.lt_trans H H')); reflexivity
                   end.

Lemma gsoLockSet_12 : forall tp b b' ofs ofs' pmap, ~ adr_range (b,ofs) LKSIZE (b',ofs') -> (Maps.PMap.get b' (lockSet (updLockSet tp (b,ofs) pmap))) ofs' = (Maps.PMap.get b' (lockSet tp)) ofs'.