Notation rsNext_In :=
  (fun (x : Clock) (gt_x_kt1 : gt_Ck x kt1) (lt_x_kt2 : lt_Ck x kt2)
     (sc_y : S_Ck SC) (sg_z : S_Ck SG) =>
   rsNext (rsIni TrGlobal (Near, x, (sc_y, sg_z)))
     (tGl_In (ttIn (x:=x) gt_x_kt1 lt_x_kt2) sc_y sg_z)) 
  (only parsing).Notation rsNext_Down :=
  (fun (z : Clock) (lt_z_kg1 : lt_Ck z kg1) (st_x : S_Ck ST) (sc_y : S_Ck SC) =>
   rsNext (rsIni TrGlobal (st_x, (sc_y, (Lowering, z))))
     (tGl_Down (tgDown lt_z_kg1) st_x sc_y)) (only parsing).Notation rsNext_Up :=
  (fun (z : Clock) (ge_z_kg2 : ge_Ck z kg2) (lt_z_kg3 : lt_Ck z kg3)
     (st_x : S_Ck ST) (sc_y : S_Ck SC) =>
   rsNext (rsIni TrGlobal (st_x, (sc_y, (Raising, z))))
     (tGl_Up (tgUp ge_z_kg2 lt_z_kg3) st_x sc_y)) (only parsing).Notation rs_Next_Approach :=
  (fun (x y : Clock) (sg_z : S_Ck SG) =>
   rsNext StGlobal (rsIni StGlobal TrGlobal (Far, x, (Sc1, y, sg_z)))
     (tGl_Approach (ttApproach x) (tcApproach y) sg_z)) 
  (only parsing).Notation rsNext_Exit :=
  (fun (x y : Clock) (lt_x_kt2 : lt_Ck x kt2) (sg_z : S_Ck SG) =>
   rsNext (rsIni TrGlobal (Inside, x, (Sc3, y, sg_z)))
     (tGl_Exit (ttExit lt_x_kt2) (tcExit y) sg_z)) 
  (only parsing).Notation rsNext_Lower :=
  (fun (y z : Clock) (eq_y_kc1 : eq_Ck y kc1) (st_x : S_Ck ST) =>
   rsNext (rsIni TrGlobal (st_x, (Sc2, y, (Open, z))))
     (tGl_Lower (tcLower eq_y_kc1) (tgLower z) st_x)) 
  (only parsing).Notation rsNext_Raise :=
  (fun (y z : Clock) (lt_y_kc2 : lt_Ck y kc2) (st_x : S_Ck ST) =>
   rsNext (rsIni TrGlobal (st_x, (Sc4, y, (Closed, z))))
     (tGl_Raise (tcRaise lt_y_kc2) (tgRaise z) st_x)) 
  (only parsing).Ltac SplitTrans' :=
  intros s1 s2 l rs_s1 p_s1 tr_gl; generalize (rsNext rs_s1 tr_gl);
   generalize rs_s1; clear rs_s1; generalize p_s1; 
   clear p_s1; elim tr_gl.Ltac SplitTrans'_Simpl :=
  SplitTrans';
   [ Simpl_In
   | Simpl_Down
   | Simpl_Up
   | Simpl_Approach
   | Simpl_Exit
   | Simpl_Lower
   | Simpl_Raise
   | Simpl_Tick ].Ltac ExistsHere_ITick s :=
  apply exists_ with (tr := TrGlobal) (P := InvTick) (1 := rsIni TrGlobal s).

Lemma NonZeno : ForAll TrGlobal SiniTCG (fun s : StGlobal => Exists TrGlobal s InvTick).