Prove2Me

lean_workbook_plus_55001

Proved

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

Prove that a(a+1)(b+1)+b(b+1)(c+1)+c(c+1)(a+1)≥34\frac{a}{(a + 1)(b + 1)} +\frac{ b}{(b + 1)(c + 1)} + \frac{c}{(c + 1)(a + 1)} \ge \frac34 where a,ba, b and cc are positive real numbers satisfying abc=1abc = 1 .

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_55001 (a b c : ℝ) (ha : a > 0 ∧ b > 0 ∧ c > 0 ∧ a * b * c = 1) : (a / (a + 1) * b + 1) + (b / (b + 1) * c + 1) + (c / (c + 1) * a + 1) ≥ 3 / 4   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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