lean_workbook_plus_56543

Proved

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

Let $a=x+y,b=y+z$ and $c=z+x$ . Then the equality becomes $2z=\frac{2(y+z)^2(z+x)}{(2x+y+z)^2}+\frac{2(z+x)^2(y+z)}{(2y+x+z)^2}\Rightarrow z=\frac{(y+z)^2(z+x)}{(2x+y+z)^2}+\frac{(y+z)(z+x)^2}{(2y+x+z)^2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_56543 :
  ∀ x y z : ℝ,
    2 * z = (2 * (y + z) ^ 2 * (z + x)) / (2 * x + y + z) ^ 2 + (2 * (z + x) ^ 2 * (y + z)) / (2 * y + x + z) ^ 2 ↔
    z = ((y + z) ^ 2 * (z + x)) / (2 * x + y + z) ^ 2 + ((y + z) * (z + x) ^ 2) / (2 * y + x + z) ^ 2   :=  by sorry

Source

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

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