reserve x,y,z,a,b,c,X,X1,X2,Y,Z for set,
  W,W1,W2 for Tree,
  w,w9 for Element of W,
  f for Function,
  D,D9 for non empty set,
  i,k,k1,k2,l,m,n for Nat,
  v,v1,v2 for FinSequence,
  p,q,r,r1,r2 for FinSequence of NAT;

theorem Th20:
  {{}} is Chain of W
proof
 {} in W by TREES_1:22;
  then reconsider S = {{}} as Subset of W by ZFMISC_1:31;
 S is Chain of W
  proof
    let p,q;
    assume that
A1: p in S and
A2: q in S;
 p = {} by A1,TARSKI:def 1;
    hence thesis by A2,TARSKI:def 1;
  end;
  hence thesis;
end;
