A quadratic difference bounds a weighted linear square

Proved

WorkbookSource.base_16693

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that

a^2+2b^2+c^2+ ab-ca\geq \frac{5}{32}(a+3b+c)^2

Source: InternLM Lean-Workbook, record lean_workbook_16693 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16693 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 + 2 * b^2 + c^2 + a * b - c * a ≥ (5 / 32) * (a + 3 * b + c)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16693; Apache-2.0

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