lean_workbook_plus_77282

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

$f(x)=f(\frac{1}{x})$ and $f(x)$ continuous implies $f(x)=h(x)+h(\frac{1}{x})$ for $h(x)=\frac{f(x)}{2}$ and $h(x)$ is continuous

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77282 (f : ℝ → ℝ) (hf : Continuous f) (h : ∀ x, f x = f (1 / x)) : ∃ h : ℝ → ℝ, Continuous h ∧ ∀ x, f x = h x + h (1 / x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph