Prove2Me

A shifted-product and fourth-power comparison

Proved
WorkbookSource.base_6832

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

lean-workbooksource-checked

Knowing that a,b,c>0 a,b,c > 0 and a+b+c=1 a + b + c = 1 ,prove the ineq: (1+a)(1+b)(1+c)≥(1−a2)2+(1−b2)2+(1−c2)2(∗) (1 + a)(1 + b)(1 + c) \geq (1 - a^2)^2 + (1 - b^2)^2 + (1 - c^2)^2(*)

Source: InternLM Lean-Workbook, record lean_workbook_6832 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_6832 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) :  (1 + a) * (1 + b) * (1 + c) ≥ (1 - a ^ 2) ^ 2 + (1 - b ^ 2) ^ 2 + (1 - c ^ 2) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6832; Apache-2.0

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