I'm also rather confused now notationally, as I thought the convention was that \\(x \le y\\) means "given x we can get y". But it looks like we might be working in the opposite preorder:

> \[ x \le x' \textrm{ and } y \le y' \textrm{ imply } x \otimes y \le x' \otimes y' .\]

>

> **[...]** if you can get \\(x\\) from \\(x'\\) and \\(y\\) from \\(y'\\), you should be able to get \\(x\\) combined with \\(y\\) from \\(x'\\) combined with \\(y'\\).

@[Matthew](https://forum.azimuthproject.org/profile/1818/Matthew%20Doty) wrote:

> For one, we want the following equation to be true:

>

> $$H + O \leq H_2O$$

I think you might mean \\(2H\\), not \\(H\\), given that you add your inequalities later and get a \\(3H\\) term.

> \[ x \le x' \textrm{ and } y \le y' \textrm{ imply } x \otimes y \le x' \otimes y' .\]

>

> **[...]** if you can get \\(x\\) from \\(x'\\) and \\(y\\) from \\(y'\\), you should be able to get \\(x\\) combined with \\(y\\) from \\(x'\\) combined with \\(y'\\).

@[Matthew](https://forum.azimuthproject.org/profile/1818/Matthew%20Doty) wrote:

> For one, we want the following equation to be true:

>

> $$H + O \leq H_2O$$

I think you might mean \\(2H\\), not \\(H\\), given that you add your inequalities later and get a \\(3H\\) term.