proximity_inv — Mathlib

English

For complex-valued f, proximity f⁻¹ ⊤ equals proximity f 0; the proximity of the reciprocal relates to the proximity at zero of f.

Русский

Для комплекснозначной f близость f⁻¹ ⊤ равна близости f 0; близость обращения связана с близостью в нуле.

LaTeX

$$$\mathrm{proximity}(f^{-1},\top) = \mathrm{proximity}(f,0)$$$

Lean4

/-- For complex-valued `f`, establish a simple relation between the proximity functions of `f` and of
`f⁻¹`.
-/
theorem proximity_inv {f : ℂ → ℂ} : proximity f⁻¹ ⊤ = proximity f 0 := by simp [proximity_zero, proximity_top]

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