nsmul_apply — Mathlib

English

The singleton addition distributes over subtraction: a singleton at a transforms under subtraction by distributing over the coordinates, i.e., single a (b1 - b2) = single a b1 - single a b2.

Русский

Одиночное добавление распределяется по вычитанию: single a (b1 - b2) = single a b1 - single a b2.

LaTeX

$$$\text{single}(a, (b_1 - b_2)) = \text{single}(a,b_1) - \text{single}(a,b_2).$$$

Lean4

theorem nsmul_apply (n : ℕ) (f : ι →₀ M) (x : ι) : (n • f) x = n • f x :=
  rfl

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