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);

theorem
  t9 in succ t implies (tree_of_subformulae(F)).t9
  is_immediate_constituent_of (tree_of_subformulae(F)).t
proof
  assume t9 in succ t;
  then ex n st t9 = t^<*n*> & t^<*n*> in dom tree_of_subformulae(F);
  hence thesis by Th7;
end;
