lean_workbook_plus_2509

Proved

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

Prove $12(a^4+b^4+c^4)\ge12(b^2c^2+c^2a^2-a^2b^2)$ where a,b,c are sides of a triangle using Muirhead's Theorem of Inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2509 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 12 * (a ^ 4 + b ^ 4 + c ^ 4) ≥ 12 * (b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2 - a ^ 2 * b ^ 2)   :=  by sorry

Source

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

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