lean_workbook_plus_42738

⚠️ 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.

Show that there is no maximum value for the expression $\frac{a^2 + b^2 + c^2}{ab + bc + ac}$ when $a, b, c$ form the sides of a triangle.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_42738 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : ¬ (∃ max, (a^2 + b^2 + c^2) / (a * b + b * c + a * c) < max)   :=  by sorry

Quantify over the entire domain of positive strict triangle triples and assert that its ratio-value set has no greatest element. Equivalently, every such triple admits another with larger ratio; the accepted source also proves supremum2.

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

Proposed corrected statement

Quantify over the entire domain of positive strict triangle triples and assert that its ratio-value set has no greatest element. Equivalently, every such triple admits another with larger ratio; the accepted source also proves supremum2.

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.