
theorem
  for a be Real st 1 <= a holds seq_a^(a,1,0) is non-decreasing
  proof
    let a be Real;
    assume AS: 1 <= a;
    for n be Nat holds seq_a^(a,1,0).n <= seq_a^(a,1,0).(n+1)
    proof
      let n be Nat;
      L2:(seq_a^(a,1,0)).n =a to_power (1*n+0) by ASYMPT_1:def 1
      .= a to_power n;
      (seq_a^(a,1,0)).(n+1) =a to_power (1*(n+1)+0) by ASYMPT_1:def 1
      .= a to_power (n+1);
      hence thesis by L2, LC5a,AS;
    end;
    hence thesis by SEQM_3:def 8;
  end;
