Notation no_invC :=
(fun s : S_Ck SC =>
match s with
| (sc, y) => sc = Sc2 /\ ~ le_Ck y kc1 \/ sc = Sc4 /\ ~ lt_Ck y kc2
end) (only parsing).

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