lean_workbook_plus_1002

Proved

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

Given two fractions $\frac{a}{b}$ and $\frac{c}{d}$ where $a,b,c,d > 0$ and $\frac{a}{b} < \frac{c}{d}$ , prove that $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1002 (a b c d : ℝ) (hb : 0 < b) (hd : 0 < d) (h : a / b < c / d) : a / b < (a + c) / (b + d) ∧ (a + c) / (b + d) < c / d   :=  by sorry

Source

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

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