Prove2Me

A symmetric squared ratio sum is at least three fifths

Proved
WorkbookSource.base_21045

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

lean-workbooksource-checked

Prove that : ∑a2a2+(b+c)2≥35\sum {\frac{{{a^2}}}{{{a^2} + {{(b + c)}^2}}} \ge \frac{3}{5}} with a;b;c∈R+a;b;c \in {R^ + }

Source: InternLM Lean-Workbook, record lean_workbook_21045 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_21045 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : 3 / 5 ≤ a ^ 2 / (a ^ 2 + (b + c) ^ 2) + b ^ 2 / (b ^ 2 + (c + a) ^ 2) + c ^ 2 / (c ^ 2 + (a + b) ^ 2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21045; Apache-2.0

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