A sum of linear and squared pair-sum ratios is at least sixteen fifths

Proved

WorkbookSource.base_38723

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

lean-workbooksource-checked

Let $a,b,c$ are positive real numbers. Prove that

\frac{b+c}{ a}+\frac{2}{125}\left(\frac{c+a}{b}\right)^2+\frac{a+b}{ c} \ge \frac{16}{5}

Source: InternLM Lean-Workbook, record lean_workbook_38723 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38723 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / a + (2 / 125) * ((c + a) / b) ^ 2 + (a + b) / c ≥ 16 / 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38723; Apache-2.0

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