lean_workbook_plus_36054

⚠️ 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.

Replacing $a=\\sqrt[4]{6x+13};\\;b=1$ , we obtain: \n\n $\\sqrt[4]{6x+13}-1=\\dfrac{6(x+2)}{\\sqrt[4]{(6x+13)^3}+\\sqrt[4]{(6x+13)^2}+\\sqrt[4]{6x+13}+1}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_36054 : ∀ x : ℝ, (6 * x + 13) ^ (1 / 4) - 1 = (6 * (x + 2)) / ((6 * x + 13) ^ (3 / 4) + (6 * x + 13) ^ (2 / 4) + (6 * x + 13) ^ (1 / 4) + 1)   :=  by sorry

The formal statement changes or incorrectly supplies part of the source problem; the accepted note identifies a concrete witness or definitional mechanism.

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 / 4) → ^0; ^ (2 / 4) → ^0; ^ (3 / 4) → ^0).

Proposed corrected statement

Use genuine real exponents 1/4,1/2,3/4 for 6x+13, with x≥−13/6, in the source fourth-root rationalization identity.

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.