cramer_subsingleton_apply — Mathlib

English

If n is a subsingleton (i.e., there is only one index), then cramer A b i = b_i for all i.

Русский

Если размерность n — подсубстанция, тогда cramer A b i = b_i.

LaTeX

$$$$cramer(A, b)_i = b_i \\quad\\text{for Subsingleton } n.$$$

Lean4

@[simp]
theorem cramer_subsingleton_apply [Subsingleton n] (A : Matrix n n α) (b : n → α) (i : n) : cramer A b i = b i := by
  rw [cramer_apply, det_eq_elem_of_subsingleton _ i, updateCol_self]

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