theorem
  (ex t1,t2 st t1 is_a_prefix_of t2) implies G2 is_subformula_of G1
proof
  given t1,t2 such that
A1: t1 is_a_prefix_of t2;
  (tree_of_subformulae(F)).t1 = G1 & (tree_of_subformulae(F)).t2 = G2 by Def5;
  hence thesis by A1,Th13;
end;
