lean_workbook_plus_69603

⚠️ 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.

The domain of the logarithmic function is $[0,\infty)$ . Therefore,\n$2x-1>0\rightarrow x>1/2$\n$8-x<0\rightarrow x<8$\n$D: (1/2,8)$ . There are 7 integers on this interval.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_69603  (S : Finset ℕ)
  (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1 / 2 < n ∧ n < 8) :
  S.card = 7   :=  by sorry

The lower bound 1/2 is natural division, hence zero. On integer points this happens to select the same seven elements, but it does not verify the source logarithm-domain derivation, whose signs/domain prose are wrong.

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

For S={n∈ℤ:1/2<n<8}, with real comparison, prove |S|=7. If a logarithm-domain result is intended, recover the original logarithmic expression; real log requires positive arguments, and 8−x>0 (not <0) gives x<8.

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.