
theorem Four2NotPerfect:
  for k being Nat holds
    4 * k + 2 is not perfect_power
  proof
    let k be Nat;
a5: 2 * (2 * k + 1) is even;
    assume 4 * k + 2 is perfect_power; then
A2: 4 divides 4 * k + 2 by a5,FourPerfectPower;
    4 divides 4 * k; then
    4 divides 4 * k + 2 - 4 * k by A2,PREPOWER:94;
    hence thesis by INT_2:28;
  end;
