Prove2Me

A cyclic quintic bound under a cubic sum-product relation

Proved
WorkbookSource.base_18675

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

lean-workbooksource-checked

Let a,b,ca,b,c be positive reals satisfying a+b+c=abc.a+b+c=abc. ∑a(1−b2)(1−c2)≤427(a+b+c)3\sum a(1-b^2)(1-c^2) \leq \frac{4}{27}(a+b+c)^3

Source: InternLM Lean-Workbook, record lean_workbook_18675 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_18675 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = a * b * c) : a * (1 - b ^ 2) * (1 - c ^ 2) + b * (1 - c ^ 2) * (1 - a ^ 2) + c * (1 - a ^ 2) * (1 - b ^ 2) ≤ (4 / 27) * (a + b + c) ^ 3  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18675; Apache-2.0

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