A quadratic form inequality

Proved

WorkbookSource.plus_62267

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $2a^2+8b^2+5c^2\geq4ab+4ac+4bc$ given $a,b,c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_62267 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.plus_62267 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : 2*a^2 + 8*b^2 + 5*c^2 ≥ 4*a*b + 4*a*c + 4*b*c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_62267; Apache-2.0

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