theorem Th40:
  for P holds P is antichain-like
      iff for p,q st p in P & p^q in P holds p = p^q
proof
  let P;
  thus P is antichain-like implies for p,q st p in P & p^q in P holds p = p^q
    proof
    assume that A1: P is antichain-like;
    let p, q;
    assume p in P & p^q in P;
    then q = {} by A1;
    hence thesis by FINSEQ_1:34;
    end;
  thus thesis by FINSEQ_1:87;
end;
