lean_workbook_plus_28349

⚠️ Retired — specification defect

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

So $np+k\le nx<np+k+1$ and $\lfloor nx\rfloor=np+k$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_28349 (n : ℕ) (x : ℝ) (k : ℕ) (h₁ : 0 < k) (hx: k ≤ x) : ∃ n : ℕ, (n : ℝ) * x + k ≤ ⌊(n : ℝ) * x⌋ ∧ ⌊(n : ℝ) * x⌋ < (n : ℝ) * x + k + 1   :=  by sorry

The integer p is erased, n is shadowed by an existential binder, and the floor bounds are no longer the source bounds.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Given integer p,k and real x with np+k≤nx<np+k+1, prove floor(nx)=np+k; restore any original hypotheses used to establish the two inequalities.

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.