Prove2Me

A cubic product correction on a nonnegative sphere

Proved
WorkbookSource.plus_31335

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

lean-workbooksource-checked

If a,b,ca,b,c are non-negative reals such that a2+b2+c2=3a^2+b^2+c^2=3 , prove that 2(a+b+c)≥3+38(a+b)(b+c)(c+a)2(a+b+c)\ge 3+\frac{3}{8}(a+b)(b+c)(c+a)

Source: InternLM Lean-Workbook, record lean_workbook_plus_31335 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_31335 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a^2 + b^2 + c^2 = 3) : 2 * (a + b + c) ≥ 3 + 3/8 * (a + b) * (b + c) * (c + a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_31335; Apache-2.0

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