The semi-magic squares of order one

For every natural number $t$, the value $\operatorname{semiMagicCount}(1,t)$ equals $1$. Here $\operatorname{semiMagicCount}(n,t)$ is the cardinality of the set of $n\times n$ arrays whose entries lie in the finite type $\operatorname{Fin}(t+1)$ — that is, each entry is an integer between $0$ and $t$ inclusive, coerced to a natural number before use — such that every row and every column sums to $t$ (the predicate $\operatorname{IsSemiMagic}$ requires $\sum_j M_{ij}=t$ for all rows $i$ and $\sum_i M_{ij}=t$ for all columns $j$). For $n=1$ this set consists of the $1\times 1$ arrays $[a]$ with $a\in\{0,1,\dots,t\}$ whose single row-sum and single column-sum both equal $t$; this forces $a=t$, so exactly one such array exists. The theorem asserts this count is $1$ for all $t:\mathbb{N}$.