map_mul_natCast — Mathlib

English

The map I ↦ matrix (R := R) n is monotone: if I ≤ J then matrix(I) ≤ matrix(J).

Русский

Отображение I ↦ matrix n(I) монотонно: если I ≤ J, то matrix n(I) ≤ matrix n(J).

LaTeX

$$$$ \\text{Monotone}(\\mathrm{matrix}(n)),$$ i.e., if I ≤ J then I.matrix n ≤ J.matrix n.$$

Lean4

theorem map_mul_natCast {α : Type*} [NonAssocSemiring α] (A B : Matrix n n ℕ) :
    map (A * B) ((↑) : ℕ → α) = map A (↑) * map B (↑) :=
  Matrix.map_mul (f := Nat.castRingHom α)

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