lean_workbook_plus_2905

Proved

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

Let $a,b,c,d$ be real numbers such that $a,b,c\ge 1$ and $a + b + c = 4 - d$ . Prove that \n $ ab + bc + ca\ge 4 - d^2.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2905 (a b c d : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) (hc : 1 ≤ c) (habc : a + b + c = 4 - d) : a * b + b * c + c * a ≥ 4 - d ^ 2   :=  by sorry

Source

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

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