lean_workbook_plus_15864

Proved

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

Prove the following inequality:\n $\frac{|a|}{1+|a|+|b|}+\frac{|b|}{1+|a|+|b|}\leq \frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15864 : ∀ a b : ℝ, 1 + |a| + |b| ≠ 0 ∧ 1 + |a| ≠ 0 ∧ 1 + |b| ≠ 0 →
  |a| / (1 + |a| + |b|) + |b| / (1 + |a| + |b|) ≤ |a| / (1 + |a|) + |b| / (1 + |b|)   :=  by sorry

Source

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

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