Prove2Me

A sum bound for nonnegative points on the unit sphere

Proved
WorkbookSource.base_7202

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

lean-workbooksource-checked

Prove that (x+y+z)2≤2(1+yz)2 (x + y + z)^2 \leq 2(1 + yz)^2 for x,y,z≥0 x,y,z\geq 0 such that x2+y2+z2=1 x^2 + y^2 + z^2 = 1

Source: InternLM Lean-Workbook, record lean_workbook_7202 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_7202 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x ^ 2 + y ^ 2 + z ^ 2 = 1) : (x + y + z) ^ 2 ≤ 2 * (1 + y * z) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7202; Apache-2.0

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