> **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
\[ I \multimap x \le x .\]