reserve x,y,z for object, X,Y for set,
  i,k,n for Nat,
  p,q,r,s for FinSequence,
  w for FinSequence of NAT,
  f for Function;

theorem
  for T1,T2 being Tree holds ^T1 with-replacement (<*0*>,T2) = ^T2
proof
  let T1,T2 be Tree;
A1: len {} = 0;
A2: <*T1*> = {}^<*T1*> by FINSEQ_1:34;
A3: <*T2*> = {}^<*T2*> by FINSEQ_1:34;
A4: <*T1*> = <*T1*>^{} by FINSEQ_1:34;
  <*T2*> = <*T2*>^{} by FINSEQ_1:34;
  hence thesis by A1,A2,A3,A4,Th57;
end;
