Prove2Me

An asymmetric squared-reciprocal product inequality

Proved
WorkbookSource.base_7117

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

lean-workbooksource-checked

Let x,y,z>0,x,y,z>0, prove that: 3yzx2+2xzy2+4xyz2≥3+yx+zx+2xz+2yz.\frac{3yz}{x^2}+\frac{2xz}{y^2}+\frac{4xy}{z^2} \geq 3+\frac{y}{x}+\frac{z}{x}+\frac{2x}{z}+\frac{2y}{z}.

Source: InternLM Lean-Workbook, record lean_workbook_7117 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_7117 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : 3 * y * z / x ^ 2 + 2 * x * z / y ^ 2 + 4 * x * y / z ^ 2 ≥ 3 + y / x + z / x + 2 * x / z + 2 * y / z  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7117; Apache-2.0

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