
theorem ABCD:
  for a,b,c,d be positive Real, n be Real st (a + b = c + d & a*b = c*d) holds
  a to_power n + b to_power n = c to_power n + d to_power n
  proof
    let a,b,c,d be positive Real, n be Real such that
    A1: a + b = c + d & a*b = c*d;
    A2:  max (a,b) = max (c,d) by A1,ISM;
    ((max (a,b) = a & min (a,b) = b) or (max (a,b) = b & min (a,b) = a)) &
    ((max (c,d) = c & min (c,d) = d) or (max (c,d) = d & min (c,d) = c))
      by XXREAL_0:def 9,def 10;
    hence thesis by A1,A2;
  end;
