
theorem
  for a,b be Nat st a <= b holds
    seq_n^ a in Big_Oh (seq_n^ b)
  proof
    let a,b be Nat;
    assume AS: a <= b;
    per cases by AS,XXREAL_0:1;
    suppose a = b;
      hence thesis by ASYMPT_0:10;
    end;
    suppose a <b;
      hence thesis by FROMASYMPT1t11;
    end;
  end;
