lean_workbook_plus_14274

Proved

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

Prove that $4\sum a^{3}b^{2}=4.\sum \frac{a^{2}b^{2}}{bc}\geq 4.\sum(ab+bc+ca)$ , given $a, b, c$ are positive reals and $abc=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14274 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a * b * c = 1) : 4 * (a ^ 3 * b ^ 2 + b ^ 3 * c ^ 2 + c ^ 3 * a ^ 2) ≥ 4 * (a * b + b * c + c * a)   :=  by sorry

Source

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

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