normalizedFactors_pow — Mathlib

English

For any irreducible p and any k ∈ ℕ, normalizedFactors(p^k) = replicate k (normalize p).

Русский

Для иррeдубрeдимоe p и любого k ∈ ℕ, normalizedFactors(p^k) = повторить k (normalize p).

LaTeX

$$normalizedFactors(p^k) = \text{replicate k} (normalize p)$$

Lean4

theorem _root_.Irreducible.normalizedFactors_pow {p : α} (hp : Irreducible p) (k : ℕ) :
    normalizedFactors (p ^ k) = Multiset.replicate k (normalize p) := by
  rw [UniqueFactorizationMonoid.normalizedFactors_pow, normalizedFactors_irreducible hp, Multiset.nsmul_singleton]

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