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

Lemma InvC' : forall s : S_Ck SC, match s with | (sc, y) => sc = Sc1 \/ sc = Sc2 /\ le_Ck y kc1 \/ sc = Sc3 \/ sc = Sc4 /\ lt_Ck y kc2 -> InvC s end.