lean_workbook_plus_54546

Proved

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

Let $a$ , $b$ , $c$ be the lengts of the sides of a triangle. Prove that ${3\over 2}a^2\geq ab+ac-bc$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54546 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 3 / 2 * a ^ 2 ≥ a * b + a * c - b * c   :=  by sorry

Source

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

View graph