reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;
reserve T,T1 for Tree;
reserve fT,fT1 for finite Tree;
reserve t for Element of T;
reserve w for FinSequence;
reserve t1,t2 for Element of T;

theorem
  width elementary_tree 0 = 1
proof
  set T = elementary_tree 0;
 now reconsider X = D as AntiChain_of_Prefixes of T by Th37;
    take X;
    thus 1 = card X by CARD_1:30;
    let Y be AntiChain_of_Prefixes of T;
 Y c= X by Def11,Th28;
    hence card Y <= card X by NAT_1:43;
  end;
  hence thesis by Def13;
end;
