A quadratic-form comparison in three variables

Proved

WorkbookSource.base_3684

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

lean-workbooksource-checked

prove that ; $(x+y)^2+13(x^2+y^2)+14z^2-2xy \ge x^2+4xy+4y^2+9z^2+6xz+12yz$ $\forall x,y,z >0$

Source: InternLM Lean-Workbook, record lean_workbook_3684 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3684 (x y z : ℝ) : (x + y) ^ 2 + 13 * (x ^ 2 + y ^ 2) + 14 * z ^ 2 - 2 * x * y ≥ x ^ 2 + 4 * x * y + 4 * y ^ 2 + 9 * z ^ 2 + 6 * x * z + 12 * y * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3684; Apache-2.0

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