cfc_nonpos — Mathlib

English

The map cfcHomSuperset ha hs is continuous when HS is a spectrum subset.

Русский

Отображение cfcHomSuperset ha hs непрерывно при подмножестве спектра HS.

LaTeX

$$Continuous (cfcHomSuperset ha hs)$$

Lean4

theorem cfc_nonpos (f : R → R) (a : A) (h : ∀ x ∈ spectrum R a, f x ≤ 0) : cfc f a ≤ 0 :=
  by
  by_cases hf : ContinuousOn f (spectrum R a)
  · simpa using cfc_mono h
  · simp only [cfc_apply_of_not_continuousOn _ hf, le_rfl]

Похожие утверждения