theorem Th4:
  len(L,{}H) = 0
proof
  set s = Partial_seq(L,{}H);
A1: for n being Nat holds s.n = 0*n+0 by Def24;
  for n holds Partial_Sums(s).n = 0
  proof
    let n;
A2: s.0 = 0 by Def24;
    Partial_Sums(s).n = (n+1)*(s.0 + s.n)/2 by A1,SERIES_2:42
      .= (n+1)*(0+0)/2 by A2,Def24;
    hence thesis;
  end;
  hence thesis;
end;
