lean_workbook_plus_31963

⚠️ 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.

Find the image of the left half plane $Re(z)<0$ under the mapping $f(z)=(z+i)/(z-i)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_31963 (f : ℂ → ℂ) (h : ∀ z, f z = (z + Complex.I) / (z - Complex.I)) : ∀ z, (z.im > 0 ∨ z.im = 0 ∧ z.re < 0) ↔ (f z).im > 0   :=  by sorry

The source left half-plane was replaced by an unrelated quadrant predicate, and the image sign is wrong.

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

Proposed corrected statement

For F(z)=(z+i)/(z−i), prove F maps{Re z<0} onto{Im w<0}, with the pole excluded as necessary and the inverse map explicitly defined.

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.