A sum bound under linked quadratic relations

Proved

WorkbookSource.base_11503

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

lean-workbooksource-checked

Let $a,b,c\ge 0,a^2+2b=c$ and $b^2+2c=a.$ Prove that

a+b+c\le \frac{3}{4}

Source: InternLM Lean-Workbook, record lean_workbook_11503 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11503 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a^2 + 2 * b = c) (hbc : b^2 + 2 * c = a) : a + b + c ≤ 3 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11503; Apache-2.0

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