A quartic pair-product sum bounds cyclic cubic and quadratic terms

Proved

WorkbookSource.base_19001

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

lean-workbooksource-checked

Given $a, b, c$ are the real numbers satisfy $a+b+c=3$ . Prove that: $3+a^2b^2+b^2c^2+c^2a^2 \ge ab^2+bc^2+ca^2+ab+bc+ca$

Source: InternLM Lean-Workbook, record lean_workbook_19001 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_19001 (a b c : ℝ) (h : a + b + c = 3) :
  3 + a^2 * b^2 + b^2 * c^2 + c^2 * a^2 ≥ a * b^2 + b * c^2 + c * a^2 + a * b + b * c + c * a  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19001; Apache-2.0

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