An asymmetric pairwise-product bound

Proved

WorkbookSource.plus_39593

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

lean-workbooksource-checked

Let $a,b,c \geq 0$ and $a+b+c=3.$ Prove that $ab+ca +\frac{13}{3}\geq bc$

Source: InternLM Lean-Workbook, record lean_workbook_plus_39593 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_39593 (a b c: ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 3) : a * b + c * a + 13 / 3 ≥ b * c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_39593; Apache-2.0

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