lean_workbook_plus_31850

Proved

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

Prove that for a triangle with side lengths $a, b, c$ , $3(ab+bc+ca)\leq (a+b+c)^2<4(ab+bc+ca)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31850 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : 3 * (a * b + b * c + c * a) ≤ (a + b + c) ^ 2 ∧ (a + b + c) ^ 2 < 4 * (a * b + b * c + c * a)   :=  by sorry

Source

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

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