lean_workbook_plus_1592

⚠️ 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.

$\frac{1}{\sqrt[3]{t}\sqrt{1+t^2+(1-t)^2}}\geq \frac{\sqrt{3}}{2^{\frac 56}(t+1)}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_1592 : ∀ t > 0, (1 / (t^(1 / 3) * (1 + t^2 + (1 - t)^2))) ≥ (Real.sqrt 3 / (2^(5 / 6) * (t + 1)))   :=  by sorry

Natural fractional exponents collapse and the square root of the second denominator factor is missing.

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

Confirmed directly from the Lean text: the numeric-literal exponents carry no type ascription, so they elaborate at type ℕ where division truncates (^(1 / 3) → ^0; ^(5 / 6) → ^0).

Proposed corrected statement

For t>0 restore1/(∛t·√(1+t²+(1−t)²))≥√3/(2^(5/6)(t+1)), with explicitly real power5/6 and genuine positive cube root; verify the source inequality in that domain.

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.