
theorem LMXFIN2:
  for d be XFinSequence of REAL
  holds for x,i be Nat st i in dom d holds
  (d (#) seq_a^(x,1,0)).i = (d.i) * x to_power (i)
  proof
    let d be XFinSequence of REAL;
    let x,i be Nat;
    assume i in dom d;
    hence (d (#) seq_a^(x,1,0)).i = (d.i) * (seq_a^(x,1,0)).i by LMXFIN1
    .= (d.i) * x to_power ((1 * i) + 0) by ASYMPT_1:def 1
    .= (d.i) * x to_power (i);
  end;
