lean_workbook_plus_71544

⚠️ 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 all functions $f:Q^+ \times Q^+ \rightarrow R$ (real) such that:\nf(1,1) = 1\nf(x,y) = f(y,x), \forall x,y \in Q^+\n(x+y)f(x,y) = yf(x,x+y), \forall x,y \in Q^+$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_71544 (f : ℚ × ℚ → ℝ) (hf : f (1, 1) = 1 ∧ ∀ x y, f (x, y) = f (y, x) ∧ (x + y) * f (x, y) = y * (f (x, x + y))) : ∀ x y, f (x, y) = 1 / (x * y)   :=  by sorry

A complete classification cannot be inferred from this counterexample alone.

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

Proposed corrected statement

Restrict the function equations to positive rational pairs and ask for the complete solution family, without the invented1/(xy) formula. f(x,y)=xy is at least one necessary member.

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.