units_conjugate' — Mathlib

English

The equivalence between pre-quasiregular elements of a product and the product of pre-quasiregular elements.

Русский

Эквивалентность между пред- quasiregular-элементами произведения и произведением таких элементов.

LaTeX

$$$\text{PreQuasiregular}(A \times B) \cong* \text{PreQuasiregular}(A) \times \text{PreQuasiregular}(B)$$$

Lean4

/-- Conjugation by a unit preserves the spectrum, inverse on left. -/
@[simp]
theorem units_conjugate' {a : A} {u : Aˣ} : spectrum R (u⁻¹ * a * u) = spectrum R a := by
  simpa using spectrum.units_conjugate (u := u⁻¹)

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