A sum and pairwise-product bound on a sphere

Proved

WorkbookSource.base_30098

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

lean-workbooksource-checked

Given $x, y, z > 0$ and $x^2 + y^2 + z^2 = 3$ , prove that $2(x + y + z) - xy - yz - xz \leq \frac{7}{2}$ .

Source: InternLM Lean-Workbook, record lean_workbook_30098 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30098 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x^2 + y^2 + z^2 = 3) : 2 * (x + y + z) - x * y - y * z - x * z ≤ 7 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30098; Apache-2.0

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