A squared pair-product sum bounds a triple-product term

Proved

WorkbookSource.base_54067

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

lean-workbooksource-checked

Prove that $(xy+yz+zx)^2+3 \geq 12xyz$ given $x+y+z=3$ .

Source: InternLM Lean-Workbook, record lean_workbook_54067 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_54067 (x y z : ℝ) (h : x + y + z = 3) :
  (x * y + y * z + z * x) ^ 2 + 3 ≥ 12 * x * y * z  :=  by sorry

Source