lean_workbook_plus_57937

Proved

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

Show that if $a,b,c>0$ and $abc=1$ , then \n\n $\frac{1}{ab+a+1}+\frac{1}{bc+b+1}+\frac{1}{ca+c+1} =1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57937 (a b c : ℝ) (h1 : a>0 ∧ b>0 ∧ c>0 ∧ a * b * c = 1) : 1 / (a * b + a + 1) + 1 / (b * c + b + 1) + 1 / (c * a + c + 1) = 1   :=  by sorry

Source

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

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