KöMaL 2012 B4461

Let $p \ge$2 be a real number. Prove that ($x$+$y$)$^p$+($z$+$v$)$^p$+($x$+$z$)$^p$+($y$+$v$)$^p \le x^p$+$y^p$+$z^p$+$v^p$+($x$+$y$+$z$+$v$)$^p$ for all non-negative real numbers $x$, $y$, $z$and $v$.