theorem Th129:
  for t,t1 being Tree, xi being Element of t holds
  (t with-replacement(xi,t1))|xi = t1
  proof
    let t,t1 be Tree;
    let xi be Element of t;
    let p be FinSequence of NAT;
A1: xi in t with-replacement(xi,t1) by TREES_1:def 9;
    hereby assume p in (t with-replacement(xi,t1))|xi;
      then xi^p in t with-replacement(xi,t1) by A1,TREES_1:def 6;
      hence p in t1 by Th01;
    end;
    assume p in t1;
    then xi^p in t with-replacement(xi,t1) by TREES_1:def 9;
    hence thesis by A1,TREES_1:def 6;
  end;
