theorem
  t1^s is Entry_Point_in_Subformula_Tree of G2 implies s in G1
  -entry_points_in_subformula_tree_of G2
proof
  consider t9 being FinSequence such that
A1: t9 = t1^s;
  (tree_of_subformulae(F)).t1 = G1 by Def5;
  then
A2: t1 in F-entry_points_in_subformula_tree_of G1 by Def3;
  assume t1^s is Entry_Point_in_Subformula_Tree of G2;
  then
  t9 in { t2 where t2 is Entry_Point_in_Subformula_Tree of G2 : t2 = t2 }
  by A1;
  then t9 in entry_points_in_subformula_tree(G2) by Th36;
  hence thesis by A2,A1,Th28;
end;
