English
QuasispectrumRestricts a f is equivalent to SpectrumRestricts (a : Unitization S A) f.
Русский
QuasispectrumRestricts a f эквивалентно SpectrumRestricts (a : Unitization S A) f.
LaTeX
$$$ QuasispectrumRestricts a f \\iff SpectrumRestricts (a : Unitization S A) f $$$
Lean4
theorem quasispectrumRestricts_iff_spectrumRestricts_inr (S : Type*) {R A : Type*} [Semifield R] [Field S]
[NonUnitalRing A] [Algebra R S] [Module R A] [Module S A] [IsScalarTower S A A] [SMulCommClass S A A]
[IsScalarTower R S A] {a : A} {f : S → R} :
QuasispectrumRestricts a f ↔ SpectrumRestricts (a : Unitization S A) f := by
rw [quasispectrumRestricts_iff, spectrumRestricts_iff, ← Unitization.quasispectrum_eq_spectrum_inr']