Prove2Me

A shifted squared reciprocal sum at fixed sum six

Proved
WorkbookSource.base_46110

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

lean-workbooksource-checked

If a,b,ca,b,c are positive and a+b+c=6a+b+c=6 , show that (a+1b)2+(b+1c)2+(c+1a)2≥754(a+\frac{1}{b})^{2}+(b+\frac{1}{c})^{2}+(c+\frac{1}{a})^{2}\geq \frac{75}{4}

Source: InternLM Lean-Workbook, record lean_workbook_46110 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_46110 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 6) : (a + 1 / b) ^ 2 + (b + 1 / c) ^ 2 + (c + 1 / a) ^ 2 ≥ 75 / 4  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46110; Apache-2.0

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