lean_workbook_plus_55945

Proved

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

Let $a,b,c$ be positive real numbers such that $\frac{3}{a+3}+\frac{2}{b+2}+\frac{1}{c+1}=\frac{9}{4}$ .Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq 1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55945 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a * b * c = 1) : 3 / (a + 3) + 2 / (b + 2) + 1 / (c + 1) = 9 / 4 → 1 / a + 1 / b + 1 / c ≥ 1   :=  by sorry

Source

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

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