A triple-product correction to a pairwise-sum bound

Proved

WorkbookSource.base_38262

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

lean-workbooksource-checked

Prove that if $x$ , $y$ , and $z$ are positive real numbers such that $x + y + z = 3$ , then $11 + xyz \geq 4(xy + yz + zx)$ .

Source: InternLM Lean-Workbook, record lean_workbook_38262 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38262 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (h : x + y + z = 3) : 11 + x*y*z ≥ 4*(x*y + y*z + z*x)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38262; Apache-2.0

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