A difference of two absolute polynomial values

Proved

WorkbookSource.problem_56689

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

lean-workbooksource-checked

Find the value of $|2a^3 - 3a^2 - 2a + 1| - |2a^3 - 3a^2 - 3a - 2009|$ given $a = 2009$ .

Source: InternLM Lean-Workbook, record lean_workbook_56689 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_56689 (a : ℝ) (h : a = 2009) : |2*a^3 - 3*a^2 - 2*a + 1| - |2*a^3 - 3*a^2 - 3*a - 2009| = 4019  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_56689; Apache-2.0

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