lean_workbook_plus_1727

⚠️ 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 $\sum{x^{2}\over 1+x^{2}}\leq{3 \over 4}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_1727 : ∀ x : ℝ, (x^2 / (1 + x^2)) ≤ 3 / 4   :=  by sorry

The formalization replaces a source sum by one unrestricted summand; the missing context prevents an exact replacement inequality.

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

Proposed corrected statement

Restore the full sum, its index set or variables, and its original normalization.

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.