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

(* Specifications: *)
Lemma lema_InvInside : ForAll TrGlobal SiniTCG InvInside.
Lemma InvT' : forall s : S_Ck ST, match s with | (st, x) => st = Far \/ st = Near /\ lt_Ck x kt2 \/ st = Inside /\ lt_Ck x kt2 -> InvT s 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.
Lemma InvG' : forall s : S_Ck SG, match s with | (sg, z) => sg = Open \/ sg = Lowering /\ lt_Ck z kg1 \/ sg = Closed \/ sg = Raising /\ lt_Ck z kg3 -> InvG s end.
Lemma NoImpl : forall A B : Prop, (A -> B) -> ~ B -> ~ A.
Lemma not_3_and : forall A B C : Prop, ~ (A /\ B /\ C) -> ~ A \/ A /\ ~ B \/ A /\ B /\ ~ C.