A cyclic pair-product reciprocal upper bound under a symmetric constraint

Proved

WorkbookSource.base_6114

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

lean-workbooksource-checked

Following inequality is true: $x,y,z>0,xy+yz+zx+xyz=4\Rightarrow\sum\frac{xy}{2x+3y}\le\frac{1}{5}(x+y+z)$

Source: InternLM Lean-Workbook, record lean_workbook_6114 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6114 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (habc : x * y + y * z + z * x + x * y * z = 4) : (x * y) / (2 * x + 3 * y) + (y * z) / (2 * y + 3 * z) + (z * x) / (2 * z + 3 * x) ≤ (1 / 5) * (x + y + z)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6114; Apache-2.0

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