factors_mul — Mathlib

English

Factors are additive with respect to multiplication: factors(a b) = factors(a) + factors(b).

Русский

Факторы складываются по умножению: factors(a b) = factors(a) + factors(b).

LaTeX

$$factors (a * b) = factors a + factors b$$

Lean4

@[simp]
theorem factors_mul (a b : Associates α) : (a * b).factors = a.factors + b.factors :=
  by
  nontriviality α
  refine FactorSet.unique <| eq_of_factors_eq_factors ?_
  rw [prod_add, factors_prod, factors_prod, factors_prod]

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