Can we express the conditions in puzzle 169 as the diagram,

\\[
\begin{matrix}
& & \Phi(=\_{X^{op}},\leq\_Y) & & \\\\
& \Phi(x',y) & \rightarrow & \Phi(x',y') & \\\\
\Phi(\leq\_{X^{op}},=\_Y) & \downarrow & & \downarrow & \\\\
& \Phi(x,y) & \rightarrow & true &
\end{matrix}
\\]