A triangle product bound at perimeter six

Proved

WorkbookSource.base_11742

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

lean-workbooksource-checked

If $a,b,c$ are the sides of a triangle whose perimeter is equal to 6 then prove that:

$3abc+72\geq 8(ab+bc+ac)$ .

Source: InternLM Lean-Workbook, record lean_workbook_11742 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11742 {a b c : ℝ} (hx: a + b + c = 6) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 3 * a * b * c + 72 ≥ 8 * (a * b + b * c + a * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11742; Apache-2.0

View graph