Notation no_invT :=
  (fun s : S_Ck ST =>
   match s with
   | (st, x) => st = Near /\ ~ lt_Ck x kt2 \/ st = Inside /\ ~ lt_Ck x kt2
   end) (only parsing).

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