algebraMap_mem_iff — Mathlib

English

If ha = QuasispectrumRestricts a f and quasispectrum S a = quasispectrum S b, then QuasispectrumRestricts b f.

Русский

Если ha = QuasispectrumRestricts a f и quasispectrum S a = quasispectrum S b, то QuasispectrumRestricts b f.

LaTeX

$$QuasispectrumRestricts a f ∧ quasispectrum S a = quasispectrum S b ⇒ QuasispectrumRestricts b f$$

Lean4

@[simp]
theorem algebraMap_mem_iff (S : Type*) {R A : Type*} [Semifield R] [Field S] [NonUnitalRing A] [Algebra R S]
    [Module S A] [IsScalarTower S A A] [SMulCommClass S A A] [Module R A] [IsScalarTower R S A] {a : A} {r : R} :
    algebraMap R S r ∈ quasispectrum S a ↔ r ∈ quasispectrum R a := by
  simp_rw [Unitization.quasispectrum_eq_spectrum_inr' _ S a, spectrum.algebraMap_mem_iff]

Похожие утверждения