Prove2Me

Uniqueness of a solution to a real cube-root equation

Proved
WorkbookCorrected.plus_23173

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

corrected-formalizationlean-workbooksource-checked

The real equation

x+73−2x−13=x3\sqrt[3]{x+7}-\sqrt[3]{2x-1}=\sqrt[3]{x}

has exactly one solution, x=1x=1.

Formalization Note: The real cube roots are represented by their cubing equations, including negative radicands. The original formalization used natural-number division in fractional exponents. This corrected statement proves both that every solution is1 and that1 satisfies the equation.

Source: InternLM Lean-Workbook, record lean_workbook_plus_23173 (Apache-2.0).

Preamble
import Mathlib
Formal statement
theorem WorkbookCorrected.plus_23173 : ∀ (x : ℝ),
    (∃ u v w : ℝ, u^3=x+7 ∧ v^3=2*x-1 ∧ w^3=x ∧ u-v=w) ↔ x=1 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_23173; Apache-2.0

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