lean_workbook_plus_9230

Proved

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

$f(x)=0$ if $x\geq\ a$ $a\geq\ 0$ and $f(x)=\frac{a}{a-x}$ for other case is the solution for $f: R^*\\to R^*$ where $R^*=R^{+}$ and 0

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9230 (a : ℝ) (ha : 0 ≤ a) : ∃ f : ℝ → ℝ, ∀ x, (x < a ∧ f x = a / (a - x)) ∨ (x ≥ a ∧ f x = 0)   :=  by sorry

Source