A functional equation with constant displacement

Proved

WorkbookSource.problem_27495

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

In $f(x)-x=f(y)-y$ , true for any $x,y\in\mathbb R$ , just choose $y=0$ and you get $f(x)-x=f(0)-0$ and so $f(x)=x+f(0)$

Source: InternLM Lean-Workbook, record lean_workbook_27495 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_27495 (f : ℝ → ℝ) (h : ∀ x y, f x - x = f y - y) : ∀ x, f x = x + f 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27495; Apache-2.0

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