A weighted square bound at fixed cyclic product sum

Proved

WorkbookSource.base_51592

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

lean-workbooksource-checked

Let $a,b,c ,d$ be real number such that $ab+bc+cd+da=1.$ Prove that

a^2+2b^2+3c^2+4d^2\geq 2.

Source: InternLM Lean-Workbook, record lean_workbook_51592 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_51592 (a b c d : ℝ) (hab : a * b + b * c + c * d + d * a = 1) :
  a ^ 2 + 2 * b ^ 2 + 3 * c ^ 2 + 4 * d ^ 2 ≥ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51592; Apache-2.0

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