theorem
  1 <= width fT
proof
   (
 ex X being AntiChain_of_Prefixes of fT st width fT = card X & for Y being
  AntiChain_of_Prefixes of fT holds card Y <= card X)&
  D is AntiChain_of_Prefixes of fT by Def13,Th37;
  then card D <= width fT;
  hence thesis by CARD_1:30;
end;
