inter_indicator_mul — Mathlib

English

For hn ≠ 0 and a ∈ M₀, the value of powMonoidWithZeroHom hn at a is a^n; i.e., powMonoidWithZeroHom hn a = a^n.

Русский

Пусть hn ≠ 0 и a ∈ M₀. Тогда powMonoidWithZeroHom hn(a) = a^n.

LaTeX

$$$ (powMonoidWithZeroHom hn) a = a^n. $$$

Lean4

theorem inter_indicator_mul (f g : ι → M₀) (i : ι) :
    (s ∩ t).indicator (fun j ↦ f j * g j) i = s.indicator f i * t.indicator g i :=
  by
  rw [← Set.indicator_indicator]
  simp_rw [indicator]
  split_ifs <;> simp

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