
theorem
  for m,k be Nat st 1 <= m holds 1 <= m to_power k
  proof
    let m,n be Nat;
    per cases;
    suppose n = 0;
      hence thesis by POWER:24;
    end;
    suppose
A1:   n <> 0;
      assume 1 <= m;
      then 1 < m or 1 = m by XXREAL_0:1;
      hence thesis by A1,POWER:26,35;
    end;
  end;
