lean_workbook_plus_38416

Proved

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

Given the same conditions, prove that $|b - c| < a$ , $|c - a| < b$ , and $|a - b| < c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38416 {a b c : ℝ} (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : |b - c| < a ∧ |c - a| < b ∧ |a - b| < c   :=  by sorry

Source

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

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