lean_workbook_plus_62549

Proved

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

Let $a+b=x,b+c=y,c+a=z$ Then $\frac{(a-b)(b-c)(c-a)}{(a+b)(b+c)(c+a)}=\frac{(z-y)(x-z)(y-x)}{xyz}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_62549 (a b c x y z : ℝ) (h1 : a + b = x) (h2 : b + c = y) (h3 : a + c = z) : (a - b) * (b - c) * (c - a) / (a + b) / (b + c) / (a + c) = (z - y) * (x - z) * (y - x) / (x * y * z)   :=  by sorry

Source

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

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