Prove2Me

Rewriting a quotient of inverse powers

Proved
WorkbookSource.problem_10526

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

lean-workbooksource-checked

We know that a−1b−1a−3−b−3=11a3−1b3⋅(1ab) \dfrac{a^{ - 1}b^{ - 1}}{a^{ - 3} - b^{ - 3}} = \dfrac{1}{\dfrac{1}{a^3} - \dfrac{1}{b^3}} \cdot \left( \dfrac{1}{ab}\right)

Source: InternLM Lean-Workbook, record lean_workbook_10526 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_10526  (a b : ℝ)
  (h₀ : a ≠ 0)
  (h₁ : b ≠ 0)
  (h₂ : a ≠ b) :
  (a⁻¹ * b⁻¹) / (a⁻¹ ^ 3 - b⁻¹ ^ 3) = 1 / ((1 / a^3) - (1 / b^3)) * (1 / (a * b))  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10526; Apache-2.0

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