reserve A for QC-alphabet;
reserve n,k,m for Nat;
reserve F,G,G9,H,H9 for Element of QC-WFF(A);
reserve t, t9, t99 for Element of dom tree_of_subformulae(F);
reserve x for set;
reserve x,y for set;
reserve t for Element of dom tree_of_subformulae(F),
  s for Element of dom tree_of_subformulae(G);
reserve t for Element of dom tree_of_subformulae(F),
  s for FinSequence;

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;
