
theorem
  for f be Real_Sequence holds f |_ Seg 0 = seq_const 0
  proof
    let f be Real_Sequence;
    set ff = f |_ Seg 0;
    set g = seq_const 0;
    for x be Element of NAT holds ff.x = g.x
    proof
      let x be Element of NAT;
      not x in dom (f | Seg 0);
      hence thesis by FUNCT_4:11;
    end;
    hence thesis by FUNCT_2:63;
  end;
