theorem
  for t being compound Element of Free(S,X) holds
  t = (main-constr t)-term args t
  proof let t be compound Element of Free(S,X);
    consider o,p such that
A1: t = o-term p by Th17;
    [o,the carrier of S]-tree p = t = (t.{})-tree args t
    by A1,ABCMIZ_A:def 10;
    then args t = p & [o, the carrier of S]`1 = (t.{})`1 = main-constr t
    by TREES_4:15,ABCMIZ_A:def 9;
    hence thesis by A1;
  end;
