lean_workbook_plus_48848

Proved

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

Let $a$ and $b$ be real numbers with $0\le a, b\le 1$ . Prove that

\frac{a}{b + 1}+\frac{kb}{a + 1}\le k

Where $k\geq 1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48848 (a b : ℝ) (hab : 0 ≤ a ∧ 0 ≤ b ∧ a + b ≤ 1) (k : ℝ) (hk : k ≥ 1) : a / (b + 1) + k * b / (a + 1) ≤ k   :=  by sorry

Source