theorem Th16:
  (ex s,x st t = x-term) or ex o,p st t = o-term p
  proof
    reconsider u = t as Term of S,X by MSAFREE4:42;
    per cases by MSATERM:2;
    suppose ex s, x st u.{} = [x,s];
      then consider s,x such that
A0:   u.{} = [x,s];
      u = root-tree [x,s] = x-term by A0,MSATERM:5;
      hence thesis;
    end;
    suppose u.{} in [:the carrier' of S,{the carrier of S}:];
      then consider a,b being object such that
A1:   a in the carrier' of S & b in {the carrier of S} & u.{} = [a,b]
      by ZFMISC_1:def 2;
      reconsider a as OperSymbol of S by A1;
      b = the carrier of S by A1,TARSKI:def 1;
      then consider p being ArgumentSeq of Sym(a,X) such that
A2:   u = [a,the carrier of S]-tree p by A1,MSATERM:10;
      Free(S,X) = FreeMSA X by MSAFREE3:31;
      then reconsider p as Element of Args(a,Free(S,X)) by INSTALG1:1;
      u = a-term p by A2;
      hence thesis;
    end;
  end;
