lean_workbook_plus_15091

⚠️ 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.

Find numerical sequence $(u_{n})$ , $n\in N$ s.t : 1) $(\forall n\in N): u_{n}\geq{1}$ , 2) $(\forall n\in N): (n+1)u_{n}\leq{n.u_{n+1}}$ , 3) $(\forall n,m\in N):u_{nm}=u_{n}.u_{m}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_15091 : ∃ u : ℕ → ℕ, (∀ n, 1 ≤ u n ∧ ∀ n, (n + 1) * u n ≤ n * u (n + 1) ∧ ∀ n m, u (n * m) = u n * u m)   :=  by sorry

The n=0 inequality forces u₀≤0 despite u₀≥1; a positive-index sequence problem was extended to zero.

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

Proposed corrected statement

Use positive integer indices n,m≥1 in all three conditions; ask for/classify such sequences, with u_n=n as a concrete consistent candidate.

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.