permanent_eq_elem_of_subsingleton

English

If n is subsingleton, then for any k in n, permanent(A) = A_{kk}. In particular, permanent(A) = A_{ii} for any i.

Русский

Если n — подпустое множество (Subs.), то для любого k ∈ n выполняется permanent(A) = A_{kk}. В частности, permanent(A) = A_{ii} для любого i.

LaTeX

$$$[Subsingleton\\ n] \\Rightarrow \\forall k \\in n, \\operatorname{permanent}(A) = A_{kk}$$$

Lean4

theorem permanent_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) : permanent A = A k k :=
  by
  have := uniqueOfSubsingleton k
  convert permanent_unique A

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