Prove2Me

A shifted quadratic reciprocal bound at fixed sum three

Proved
WorkbookSource.base_923

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

lean-workbooksource-checked

Let a,b,c>0,a+b+c=3a, b, c >0, a + b + c = 3 . Prove that: (a+1)2(b+1)2c2+1+(a+1)2(c+1)2b2+1+(b+1)2(c+1)2a2+1≥24\dfrac{(a+1)^2(b+1)^2}{c^2+1} + \dfrac{(a+1)^2(c+1)^2}{b^2+1} + \dfrac{(b+1)^2(c+1)^2}{a^2+1} \geq 24

Source: InternLM Lean-Workbook, record lean_workbook_923 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_923 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a + 1) ^ 2 * (b + 1) ^ 2 / (c ^ 2 + 1) + (a + 1) ^ 2 * (c + 1) ^ 2 / (b ^ 2 + 1) + (b + 1) ^ 2 * (c + 1) ^ 2 / (a ^ 2 + 1) ≥ 24  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_923; Apache-2.0

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