Prove2Me

A cyclic linear-over-quadratic lower bound at fixed sum three

Proved
WorkbookSource.base_6003

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

lean-workbooksource-checked

Let a,b and c tree positives reels such that a+b+c=3a+b+c=3 ; prove that : ab2+c+bc2+a+ca2+b≥3/2\frac{a}{b^2+c} + \frac{b}{c^2+a} + \frac{c}{a^2+b} \ge 3/2

Source: InternLM Lean-Workbook, record lean_workbook_6003 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_6003 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a / (b ^ 2 + c) + b / (c ^ 2 + a) + c / (a ^ 2 + b) ≥ 3 / 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6003; Apache-2.0

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