Prove2Me

A weighted squared ratio sum is at least three

Proved
WorkbookSource.base_28417

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

lean-workbooksource-checked

If a,b,ca,b,c are positive real numbers, then (a+3b+3c)237a2+3(b+c)2+(b+3c+3a)237b2+3(c+a)2+(c+3a+3b)237c2+3(a+b)2≥3.\frac{(a+3b+3c)^2}{37a^2+3(b+c)^2}+\frac{(b+3c+3a)^2}{37b^2+3(c+a)^2}+\frac{(c+3a+3b)^2}{37c^2+3(a+b)^2}\ge3.

Source: InternLM Lean-Workbook, record lean_workbook_28417 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_28417 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + 3 * b + 3 * c) ^ 2 / (37 * a ^ 2 + 3 * (b + c) ^ 2) + (b + 3 * c + 3 * a) ^ 2 / (37 * b ^ 2 + 3 * (c + a) ^ 2) + (c + 3 * a + 3 * b) ^ 2 / (37 * c ^ 2 + 3 * (a + b) ^ 2) ≥ 3  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28417; Apache-2.0

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