Monotonicity of a rational function on nonnegative inputs

Proved

WorkbookSource.problem_32497

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

The 2nd, if $0\le a\le b$ , then $\frac{a}{1+a}\le\frac{b}{1+b}$ .

Source: InternLM Lean-Workbook, record lean_workbook_32497 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_32497  (a b : ℝ)
  (h₀ : 0 ≤ a ∧ a ≤ b) :
  a / (1 + a) ≤ b / (1 + b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32497; Apache-2.0

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