lean_workbook_plus_15594

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $a,b,c$ are the lengths of triangle sides, prove that $abc\ge (a+b-c)(b+c-a)(c+a-b)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15594 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : a * b * c ≥ (a + b - c) * (b + c - a) * (c + a - b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph