Prove2Me

lean_workbook_plus_82832

Proved

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

proofwiki

f(x)=−x∀x≤0f(x)=-x\quad\forall x\le 0 and f(x)=x−h(x)∀x>0f(x)=x-h(x)\quad\forall x>0, whatever is continuous function h(x)h(x) from [0,+∞)→(−∞,0][0,+\infty)\to(-\infty,0] with h(0)=0h(0)=0

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_82832 (h : ℝ → ℝ) (hcont : Continuous h) (h₀ : h 0 = 0) (x : ℝ) : ∃ f : ℝ → ℝ, Continuous f ∧ ∀ y ≤ 0, f y = -y ∧ ∀ y > 0, f y = y - h y   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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