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.