A quartic sum bound for positive variables

Proved

WorkbookCorrected.base_10876

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

corrected-formalizationlean-workbooksource-checked

Let $a,b,c,d$ be positive reals. Prove that: $(a+b+c)^4\geq16(a^2b^2+b^2c^2+c^2a^2)+11abc(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_10876 (Apache-2.0). Natural-language proposition preserved; missing source domain assumptions restored. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_10876 (a b c d : ℝ) (source_domain_d : 0 < d) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 4 ≥ 16 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) + 11 * a * b * c * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10876; Apache-2.0

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