lean_workbook_plus_17427

Proved

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

Prove that $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} < 2$ where a,b,c are the sides of a triangle.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17427 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a / (b + c) + b / (a + c) + c / (a + b) < 2   :=  by sorry

Source

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

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