lean_workbook_plus_68053

⚠️ 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.

Prove that there is no function $f: \mathbb{N}\rightarrow \mathbb{N}$ such that $f(3n+1)\le f(3n+4)-1$ and $f(5n+2)\ge f(5n+7)-1\ ,\ (\forall)n\in \mathbb{N}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_68053 : ¬∃ f : ℕ → ℕ, (∀ n : ℕ, f (3 * n + 1) ≤ f (3 * n + 4) - 1) ∧ (∀ n : ℕ, f (5 * n + 2) ≥ f (5 * n + 7) - 1)   :=  by sorry

The second ordinary inequality already matches this rearrangement; the first Nat subtraction admits the zero function.

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

Proposed corrected statement

Express the first inequality as f(3n+1)+1≤f(3n+4), and the second as f(5n+7)≤f(5n+2)+1, so subtraction is interpreted in the intended integer sense.

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.