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;
