lean_workbook_plus_1312

Proved

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

Prove $\frac{1-x}{1+x}\frac{1-y}{1+y}\geq\frac{1-x-y}{1+x+y}$ for all $x,y>0,x+y<1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1312 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (hxy : x + y < 1) : (1 - x) / (1 + x) * (1 - y) / (1 + y) ≥ (1 - x - y) / (1 + x + y)   :=  by sorry

Source

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

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