Definition InvInside (s : StGlobal) :=
  match s with
  | ((st, x), _) => st = Inside -> gt_Ck x kt1
  end.

Lemma InvT' : forall s : S_Ck ST, match s with | (st, x) => st = Far \/ st = Near /\ lt_Ck x kt2 \/ st = Inside /\ lt_Ck x kt2 -> InvT s end.