reserve a,b,n for Element of NAT;

theorem Th7:
  for a, b being Real holds
  (a + b)*(a - b) = a to_power 2 - b to_power 2
proof
  let a, b be Real;
  (a + b)*(a - b) = a^2 - b^2 .= a to_power 2 - b^2 by POWER:46
    .= a to_power 2 - b to_power 2 by POWER:46;
  hence thesis;
end;
