> **Puzzle 195.** Show that in any closed monoidal poset we have \$$I \multimap x = x \$$ for every element \$$x\$$.

By the anti-symmetry property of posets we need to show:

1. \$$x \le I \multimap x \$$
2. \$$I \multimap x \le x\$$.

For the first statement, by reflexivity we have that

$x \le x$

and we apply the monoidal unit \$$I\$$ to the left side

$I \otimes x \le x$

and by the definition of closed we get

$x \le I \multimap x .$

For the second statement, by reflexivity we have that

$I \multimap x \le I \multimap x$

and we apply the definition of closed

$I \otimes (I \multimap x) \le x$

and use the fact that \$$I\$$ is the monoidal unit to get

$I \multimap x \le x .$