A shifted quadratic ratio lower bound at fixed sum three

Proved

WorkbookSource.base_17825

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

lean-workbooksource-checked

(a;b;c>0 ; $b + a + c = 3$ )prove that $\frac {a^2 + 1}{b^2 + c^2} + \frac {b^2 + 1}{a^2 + c^2} + \frac {c^2 + 1}{b^2 + a^2}\ge 3$

Source: InternLM Lean-Workbook, record lean_workbook_17825 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17825 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a^2 + 1) / (b^2 + c^2) + (b^2 + 1) / (a^2 + c^2) + (c^2 + 1) / (b^2 + a^2) ≥ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17825; Apache-2.0

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