given the binary variables: y_i, x_i, i = 1,..,5

where

$\displaystyle

\sum_{i=1}^5 x_i = \sum_{i=1}^5 y_i = 1

$

Show that

$\displaystyle

\sum_{i=1}^t x_i \leq \sum_{i = 1}^{t} y_i, t \in \{1,\dots,5\}

$

implies that:

$\displaystyle

\sum_{i=t}^5 x_i \geq \sum_{i = t}^{5} y_i, t \in \{1,\dots,5\}

$

Can anybody help me, to show that it holds for every index?