lean_workbook_plus_82585

Disproved

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

If $f(1)=0$ , $P(x-1,1)$ $\implies$ $\boxed{f(x)=1-x}$ $\forall x$ , which indeed is a solution

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82585 (f : ℝ → ℝ) (hf: f 1 = 0) (hP: ∀ x, f (x-1) + f x = 1): ∀ x, f x = 1 - x   :=  by sorry

Source