Prove2Me

A product bound under unit positive sum

Proved
WorkbookSource.base_33501

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

lean-workbooksource-checked

Let a,b,ca,b,c be positive real numbers with a+b+c=1.a+b+c=1. Show that a2+b2+c2≥abc+(a+b)(b+c)(c+a).a^2+b^2+c^2\geq abc+(a+b)(b+c)(c+a).

Source: InternLM Lean-Workbook, record lean_workbook_33501 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_33501 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : a^2 + b^2 + c^2 ≥ a * b * c + (a + b) * (b + c) * (c + a)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33501; Apache-2.0

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