factors_prod — Mathlib

English

In a UniqueFactorizationMonoid, for any nonzero a, the product of its irreducible factors is associated to a.

Русский

В уникальном факторизационном моноиде произведение непрерывно факторов ирредуцируемо к a.

LaTeX

$$$\\text{Associated}(\\operatorname{factors}(a).\\operatorname{prod} a).$$$

Lean4

theorem factors_prod {a : α} (ane0 : a ≠ 0) : Associated (factors a).prod a :=
  by
  rw [factors, dif_neg ane0]
  exact (Classical.choose_spec (exists_prime_factors a ane0)).2

Похожие утверждения