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;

theorem Th36:
  not p1,p2 are_c=-comparable implies { p1,p2 } is AntiChain_of_Prefixes-like
proof
  assume
A1: not p1,p2 are_c=-comparable;
  thus for x st x in { p1,p2 } holds x is FinSequence by TARSKI:def 2;
  let q1,q2 be FinSequence;
  assume that
A2: q1 in { p1,p2 } and
A3: q2 in { p1,p2 };
A4: q1 = p1 or q1 = p2 by A2,TARSKI:def 2;
 q2 = p1 or q2 = p2 by A3,TARSKI:def 2;
  hence thesis by A1,A4;
end;
