A four-variable quadratic lower bound at total four

Proved

WorkbookSource.plus_12056

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

lean-workbooksource-checked

Let $a,b,c,d\geq 0$ and $a+b+c+d=4 .$ Prove that

a^2+ b^2+c^2+d^2+a+bc+d \geq 7

Source: InternLM Lean-Workbook, record lean_workbook_plus_12056 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_12056 (a b c d : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) (habc : a + b + c + d = 4) : a^2 + b^2 + c^2 + d^2 + a + b*c + d ≥ 7   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_12056; Apache-2.0

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