Prove2Me

lean_workbook_plus_13141

Proved

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

Factorize we get: \n\n Q=1a+b+c(1ab+1bc+1ca)=1abc(a+b+c)(a+b+c)=1abcQ=\frac{1}{a+b+c}\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\right)=\frac{1}{abc\left(a+b+c\right)}\left(a+b+c\right)=\frac{1}{abc}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_13141  (a b c : ℝ)
  (h₀ : a ≠ 0 ∧ b ≠ 0 ∧ c ≠ 0)
  (h₁ : a + b + c = 1) :
  1 / (a * b * c * (a + b + c)) * (a + b + c) = 1 / (a * b * c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph