The mediant of two equal ratios

Proved

WorkbookSource.problem_49999

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

lean-workbooksource-checked

Given $\frac{a}{b}=\frac{c}{d}$ , prove that $\frac{a+c}{b+d}=\frac{a}{b}$ using the steps: multiply both sides by $bd$ , add $ab$ to both sides, apply the distributive property, and divide by $b(b+d)$

Source: InternLM Lean-Workbook, record lean_workbook_49999 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_49999 (a b c d : ℝ) (h₁ : b ≠ 0) (h₂ : d ≠ 0) (h₃ : b + d ≠ 0) : a / b = c / d → (a + c) / (b + d) = a / b  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_49999; Apache-2.0

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