lean_workbook_plus_81921

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c,d$ non-negative real numbers and sum of $a,b,c,d$ equal $4.$ Prove that $(a+b+c+d)^2\geqslant4(ab+bc+cd+da)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81921 (a b c d : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) (hab : a + b + c + d = 4) : (a + b + c + d) ^ 2 ≥ 4 * (a * b + b * c + c * d + d * a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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