lean_workbook_plus_16306

Proved

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

As $f(x)=x^2$ is a bijection among positive reals, we may square both sides and call it equivalent.

a^4+b^4+c^4+2\left(a^2b^2+a^2c^2+b^2c^2\right)\ge6\left(a^2 b^2+a^2c^2+b^2c^2\right)-3\left(a^4+b^4+c^4\right).

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16306 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ 4 + b ^ 4 + c ^ 4 + 2 * (a ^ 2 * b ^ 2 + a ^ 2 * c ^ 2 + b ^ 2 * c ^ 2) ≥ 6 * (a ^ 2 * b ^ 2 + a ^ 2 * c ^ 2 + b ^ 2 * c ^ 2) - 3 * (a ^ 4 + b ^ 4 + c ^ 4)   :=  by sorry

Source

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

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