lean_workbook_plus_77495

Proved

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

For $k>0$ and $0\leq a, b, c, d\leq k,$ prove that the following inequality holds \n\n $2k^2-k(a+b+c+d)+ab+bc+cd+da\geq0$ \n\n When does equality hold ?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77495 (k a b c d : ℝ) (h₁ : 0 < k) (h₂ : 0 ≤ a ∧ 0 ≤ b ∧ 0 ≤ c ∧ 0 ≤ d) (h₃ : a ≤ k ∧ b ≤ k ∧ c ≤ k ∧ d ≤ k) : 2 * k ^ 2 - k * (a + b + c + d) + a * b + b * c + c * d + d * a ≥ 0   :=  by sorry

Source

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

View graph