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.