A quadratic lower bound for nonnegative variables with total at most eight

Proved

WorkbookSource.base_41246

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

lean-workbooksource-checked

Let $a,b,c$ be non-negative real number such that $a+b+c \le 8$ , Prove that $a^2+(b-6)a-(b-2)c\ge -9.$

Source: InternLM Lean-Workbook, record lean_workbook_41246 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41246 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c ≤ 8) : a^2 + (b - 6) * a - (b - 2) * c ≥ -9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41246; Apache-2.0

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