reserve a,b,n for Element of NAT;

theorem Th6:
  for a being non zero Real holds (a to_power n) to_power 2
  = a to_power (2*n)
proof
  let a be non zero Real;
  ((a to_power n)to_power 2)=((a to_power n)to_power(1+1))
    .=((a to_power n)to_power 1)*((a to_power n)to_power 1) by FIB_NUM2:5
    .=(a to_power n)*((a to_power n)to_power 1) by POWER:25
    .=(a to_power n)*(a to_power n) by POWER:25
    .=a to_power (n+n) by FIB_NUM2:5
    .=a to_power (2*n);
  hence thesis;
end;
