theorem
  G is_subformula_of H & H is_subformula_of G implies G = H
proof
  assume that
A1: G is_subformula_of H and
A2: H is_subformula_of G;
  assume
A3: G <> H;
  then G is_proper_subformula_of H by A1;
  then
A4: len G < len H by Th62;
  H is_proper_subformula_of G by A2,A3;
  hence contradiction by A4,Th62;
end;
