lean_workbook_plus_48260

⚠️ 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.

Introducing $a = 1 + x, b = 1 + y, c = 1 + z$ would be helpful. The system becomes:\n $\begin{cases} a^2b = 1 - 2a \\ b^2c = 1 - 2b \\ c^2a = 1 - 2c \end{cases}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_48260 : ∀ x y z : ℝ, (1 + x)^2 * (1 + y) = 1 - 2 * (1 + x) ∧ (1 + y)^2 * (1 + z) = 1 - 2 * (1 + y) ∧ (1 + z)^2 * (1 + x) = 1 - 2 * (1 + z) ↔ x = y ∧ y = z ∧ z = x   :=  by sorry

A substituted system is changed to an equivalence with equality of coordinates, which lacks the scalar equation.

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 system as the substitution result; if classifying solutions, retain the common-coordinate equation a³+2a−1=0 after proving a=b=c.

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.