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 Th5:
  (for p holds p in W1 iff p in W2) implies W1 = W2
proof
  assume
A1: for p holds p in W1 iff p in W2;
  thus W1 c= W2
  proof
    let x be object;
    assume x in W1;
    then reconsider p = x as Element of W1;
 p in W2 by A1;
    hence thesis;
  end;
  let x be object;
  assume x in W2;
  then reconsider p = x as Element of W2;
 p in W1 by A1;
  hence thesis;
end;
