A comparison of weighted cyclic reciprocal sums

Proved

WorkbookSource.plus_75470

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

lean-workbooksource-checked

Let $a,b,c>0$ ,prove that: $6+2\,{\frac {c}{a}}+2\,{\frac {a}{b}}+2\,{\frac {b}{c}}\leq 3\,{\frac {bc}{{a}^{2}}}+{\frac {c}{b}}+3\,{\frac {ac}{{b}^{2}}}+{\frac {a}{c}}+3\,{\frac {ab}{{c}^{2}}}+{\frac {b}{a}}$ . BQ

Source: InternLM Lean-Workbook, record lean_workbook_plus_75470 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_75470 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 6 + 2 * c / a + 2 * a / b + 2 * b / c ≤ 3 * b * c / a ^ 2 + c / b + 3 * a * c / b ^ 2 + a / c + 3 * a * b / c ^ 2 + b / a   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_75470; Apache-2.0

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