lean_workbook_plus_220
Disproved⚠️ Retired — specification defect
The Lean statement below does not encode the problem shown on this page, so its
Disprovedstatus carries no information about that problem. Do not import this node or use it as a dependency.
=2^{2018}+\frac{(2^{2019}-1)(2^{2020}-1)-(2^{2018}-1)(2^{2019}-1)}{3}$
Why this node was retired
The posted statement is
theorem lean_workbook_plus_220 (h₁ : 0 < 2018) : 2^2018 + ((2^2019 - 1) * (2^2020 - 1) - (2^2018 - 1) * (2^2019 - 1)) / 3 = 2^2018 + (2^4038 - 2^2019 - 2^4037 + 2^2018) / 3 := by sorry
The source product difference was expanded into incorrect powers of two.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Keep the exact original expression or expand its numerator as 2^4039−2^2020−2^4037+2^2018; then simplify using exact arithmetic.
Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.
import Mathlib.Analysis.Complex.Basic
theorem lean_workbook_plus_220 (h₁ : 0 < 2018) : 2^2018 + ((2^2019 - 1) * (2^2020 - 1) - (2^2018 - 1) * (2^2019 - 1)) / 3 = 2^2018 + (2^4038 - 2^2019 - 2^4037 + 2^2018) / 3 := by sorry