lean_workbook_plus_16813

Proved

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

Find $f(a)$ given $f(x+a) = \frac{1}{2} + \sqrt{f(x) - f(x)^2}$ and $x=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16813 (f : ℝ → ℝ) (a : ℝ) (h₁ : f (0 + a) = 1 / 2 + Real.sqrt (f 0 - (f 0)^2)) : f a = 1 / 2 + Real.sqrt (f 0 - (f 0)^2)   :=  by sorry

Source

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

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