mabs_mulIndicator_symmDiff — Mathlib

English

For sets s, t and f, x, the multiplicative absolute value of the indicator on the symmetric difference equals the absolute value of the quotient of the indicators: |mulIndicator (s Δ t) f x| = |mulIndicator s f x / mulIndicator t f x|.

Русский

Для множеств s, t и функции f, приpunkции x выполняется: |mulIndicator (s Δ t) f x| = |mulIndicator s f x / mulIndicator t f x|.

LaTeX

$$|mulIndicator (s \Delta t) f x|_M = |mulIndicator s f x / mulIndicator t f x|_M$$

Lean4

@[to_additive]
theorem mabs_mulIndicator_symmDiff (s t : Set α) (f : α → M) (x : α) :
    |mulIndicator (s ∆ t) f x|ₘ = |mulIndicator s f x / mulIndicator t f x|ₘ :=
  apply_mulIndicator_symmDiff mabs_inv s t f x

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