lean_workbook_plus_24586

Disproved

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

Let a,b,c be positive reals such that $a+b+c\leq3$ . Prove that $\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\geq3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_24586 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c ≤ 3) : 1 / (1 + a) + 1 / (1 + b) + 1 / (1 + c) ≥ 3   :=  by sorry

Source

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

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