image — Mathlib

English

If SpectrumRestricts a f, then the image equality holds: Set.image(algebraMap R S)(spectrum R a) = spectrum S a.

Русский

Если SpectrumRestricts a f, то выполняется равенство образов: Set.image(algebraMap R S)(spectrum R a) = spectrum S a.

LaTeX

$$$ \\mathrm{Set.image}(\\mathrm{algebraMap} R S)(\\mathrm{spectrum} R a) = \\mathrm{spectrum} S a $$$

Lean4

theorem image (h : SpectrumRestricts a f) : f '' spectrum S a = spectrum R a := by
  simp only [← h.algebraMap_image, Set.image_image, h.left_inv _, Set.image_id']

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