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 Th5:
  F in rng tree_of_subformulae(F)
proof
  (tree_of_subformulae(F)).{} = F & {} in dom tree_of_subformulae(F) by Def2,
TREES_1:22;
  hence thesis by FUNCT_1:def 3;
end;
