A fourth-power sum with a harmonic pair-product correction

Proved

WorkbookSource.base_10405

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

The following is also true

$a,b,c>0, a+b+c=3\Longrightarrow \ \ \ a^4+b^4+c^4+\frac{15}{4} \left( \frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ca}{c+a}\right) \ge \frac{23}{8}(a^2+b^2+c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_10405 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10405 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a ^ 4 + b ^ 4 + c ^ 4 + (15 / 4) * (a * b / (a + b) + b * c / (b + c) + c * a / (c + a)) ≥ (23 / 8) * (a ^ 2 + b ^ 2 + c ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10405; Apache-2.0

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