theorem Th29:
  for F,G,H holds { t^s where t is Element of dom
  tree_of_subformulae(F), s is Element of dom tree_of_subformulae(G) : t in F
  -entry_points_in_subformula_tree_of G & s in G
-entry_points_in_subformula_tree_of H } c= F-entry_points_in_subformula_tree_of
  H
proof
  let F,G,H;
  let x be object;
  assume x in { t^s where t is Element of dom tree_of_subformulae(F), s is
  Element of dom tree_of_subformulae(G) : t in F
  -entry_points_in_subformula_tree_of G & s in G
  -entry_points_in_subformula_tree_of H };
  then
  ex t being Element of dom tree_of_subformulae(F), s being Element of dom
tree_of_subformulae(G) st x = t^s & t in F -entry_points_in_subformula_tree_of
  G & s in G -entry_points_in_subformula_tree_of H;
  hence thesis by Th27;
end;
