Prove2Me

A product comparison involving shifted squares and pairwise sums

Proved
WorkbookSource.base_28276

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

lean-workbooksource-checked

If a,b,ca,b,c are real numbers, then

(a2+12)(b2+12)(c2+12)≥(a+b−12)(b+c−12)(c+a−12).\left(a^2+\frac 1{2}\right)\left(b^2+\frac 1{2}\right)\left(c^2+\frac 1{2}\right)\ge \left(a+b-\frac 1{2}\right)\left(b+c-\frac 1{2}\right)\left(c+a-\frac 1{2}\right).

Source: InternLM Lean-Workbook, record lean_workbook_28276 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_28276 (a b c : ℝ) : (a^2 + 1/2) * (b^2 + 1/2) * (c^2 + 1/2) ≥ (a + b - 1/2) * (b + c - 1/2) * (c + a - 1/2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28276; Apache-2.0

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