A cubic symmetric bound with lower-degree terms

Proved

WorkbookSource.base_13088

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

lean-workbooksource-checked

Prove that $p(p+1)^2+12r \ge 4q(p+2)$ given $a,b,c > 0$ , $p=a+b+c$ , $q=ab+bc+ca$ , $r=abc$ .

Source: InternLM Lean-Workbook, record lean_workbook_13088 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_13088 (a b c r p q : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = r) (pq : a * b + b * c + c * a = q) (pqr : a + b + c = p) : p * (p + 1) ^ 2 + 12 * r ≥ 4 * q * (p + 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13088; Apache-2.0

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