Prove2Me

A sum minus pairwise product bound under a cubic constraint

Proved
WorkbookSource.plus_20364

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

lean-workbooksource-checked

If x,y,zx,y,z are positive real satisfy x2+y2+z2+2xyz=1x^2+y^2+z^2+2xyz=1, prove that (x+y+z)−(xy+yz+zx)≥34(x+y+z) -(xy+yz+zx) \geq \frac{3}{4}

Source: InternLM Lean-Workbook, record lean_workbook_plus_20364 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_20364 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x^2 + y^2 + z^2 + 2 * x * y * z = 1) : (x + y + z) - (x * y + y * z + z * x) ≥ 3 / 4   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_20364; Apache-2.0

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