lean_workbook_plus_50151

Proved

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

Let $a,b,c>0$ and $(a+b-c)\left(\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)=4.$ Prove that: $(a^4+b^4+c^4)\left(\frac{1}{a^4}+\frac{1}{b^4}+\frac{1}{c^4}\right)\geq 2304.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50151 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) (h : (a + b - c) * (1 / a + 1 / b - 1 / c) = 4) : (a ^ 4 + b ^ 4 + c ^ 4) * (1 / a ^ 4 + 1 / b ^ 4 + 1 / c ^ 4) ≥ 2304   :=  by sorry

Source

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

View graph