lean_workbook_plus_75459

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that $2S=k(k+1)$ where $S=k+(k-1)+\cdots+1$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_75459 (k : ℕ) : 2 * (k * (k + 1) / 2) = k * (k + 1)   :=  by sorry

The source summation S=k+(k−1)+…+1 was replaced directly by the closed form k(k+1)/2, so the target checks divisibility but not the asserted sum formula.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Define S=∑_(i=1)^k i and prove2S=k(k+1), including k=0. A separate evenness lemma may justify the quotient formula, but cannot substitute for identifying S with the sum.

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.