normalize_normalized_factor — Mathlib

English

For any a and x with x ∈ normalizedFactors a, normalize x = x.

Русский

Для любого a и x с x ∈ нормализованных факторов a, normalize x = x.

LaTeX

$$normalize(x) = x$$

Lean4

theorem normalize_normalized_factor {a : α} : ∀ x : α, x ∈ normalizedFactors a → normalize x = x :=
  by
  rw [normalizedFactors, factors]
  split_ifs with h; · simp
  intro x hx
  obtain ⟨y, _, rfl⟩ := Multiset.mem_map.1 hx
  apply normalize_idem

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