radical_associated — Mathlib

English

For a ≠ 0, primeFactors(a) = ∅ iff a is a unit.

Русский

Для a ≠ 0, primeFactors(a) = ∅ эквивалентно тому, что a — единица.

LaTeX

$$$ a \neq 0 \Rightarrow (\operatorname{primeFactors}(a) = \emptyset \iff IsUnit(a)) $$$

Lean4

theorem radical_associated (ha : IsRadical a) (ha' : a ≠ 0) : Associated (radical a) a :=
  by
  rw [radical, ← Finset.prod_val, primeFactors_val_eq_normalizedFactors ha]
  exact prod_normalizedFactors ha'

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