reserve A for QC-alphabet;
reserve n,k,m for Nat;
reserve F,G,G9,H,H9 for Element of QC-WFF(A);

theorem Th1:
  F is_subformula_of G implies len @ F <= len @ G
proof
  assume
A1: F is_subformula_of G;
  per cases;
  suppose
    F = G;
    hence thesis;
  end;
  suppose
    F <> G;
    then F is_proper_subformula_of G by A1,QC_LANG2:def 21;
    hence thesis by QC_LANG2:54;
  end;
end;
