
theorem FourPerfectPower:
  for n being even perfect_power Nat holds
    4 divides n
  proof
    let n be even perfect_power Nat;
    consider x being Nat, k being Nat such that
A1: k > 1 &
    n = x |^ k by PerPowDef;
    2 divides x by INT_2:28,NAT_3:5,A1,ABIAN:def 1;
    hence thesis by A1,FourDivPower;
  end;
