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
  not t1,t2 are_c=-comparable implies { t1,t2 } is AntiChain_of_Prefixes of T
proof
  assume not t1,t2 are_c=-comparable;
  then reconsider A = { t1,t2 } as AntiChain_of_Prefixes by Th36;
 A is AntiChain_of_Prefixes of T
  proof
    let x be object;
    assume x in A;
then  x = t1 or x = t2 by TARSKI:def 2;
    hence thesis;
  end;
  hence thesis;
end;
