 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

\b[True.] Set $l=\inf A$ and $v=\inf\{\inf R_m:m\geq1\}$. Because $R_m\subseteq A$, every row <infimum> satisfies $\inf R_m\geq l$, so $v\geq l$. But $x_{m,n}\geq\inf R_m\geq v$ for all $m,n$, making $v$ a <lower bound> of $A$. Therefore $v\leq l$, and
$$
\boxed{\inf A=\inf_{m\geq1}\inf_{n\geq1}x_{m,n}.}
$$

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