= Iterated extrema of an array
{title2=$\sup_m\sup_n x_{m,n}=\sup_{m,n}x_{m,n}$}
For a nonempty bounded array of <real numbers>, taking the <supremum> of each row and then the <supremum> of those values gives the <supremum> of all entries. Every row <supremum> is bounded by the global <supremum>; conversely, every entry is bounded by the iterated <supremum>. The same argument with <lower bounds> proves $\inf_m\inf_n x_{m,n}=\inf_{m,n}x_{m,n}$. Mixed <infima> and <suprema> satisfy the <weak minimax inequality> rather than an equality in general.
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