A shifted cyclic reciprocal product is at least 125

Proved

WorkbookSource.plus_37156

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

lean-workbooksource-checked

If $a,b,c$ are positive numbers such that $a+b+c=3$ , then

$(3a+\frac 2{b})(3b+\frac 2{c})(3c+\frac 2{a}) \ge 125$

Source: InternLM Lean-Workbook, record lean_workbook_plus_37156 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_37156 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (3 * a + 2 / b) * (3 * b + 2 / c) * (3 * c + 2 / a) ≥ 125   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_37156; Apache-2.0

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