A cubic and linear sum bound under unit product

Proved

WorkbookCorrected.base_32021

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

corrected-formalizationlean-workbooksource-checked

Let $a,b,c$ be positive real numbers such that $abc=1$ . Prove that

a+b+c+a^3+b^3+c^3\leq \frac{2}{3} (a^2+b^2+c^2)^2

Source: InternLM Lean-Workbook, record lean_workbook_32021 (Apache-2.0). Natural-language proposition preserved; missing source domain assumptions restored. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_32021 (a b c : ℝ) (source_domain_a : 0 < a) (source_domain_b : 0 < b) (source_domain_c : 0 < c) (h1 : a * b * c = 1) :
  a + b + c + a^3 + b^3 + c^3 ≤ (2 / 3) * (a^2 + b^2 + c^2)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32021; Apache-2.0

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