reserve a,b,n for Element of NAT;

theorem
  for a being Real, n being Element of NAT st a to_power n = 0
  holds a = 0
proof
  let a be Real, n be Element of NAT;
  assume a to_power n = 0;
  then
A1: a |^ n = 0 by POWER:41;
  assume a <> 0;
  hence thesis by A1,PREPOWER:5;
end;
