lean_workbook_plus_13916

⚠️ 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 an example of an injective function $f:R\rightarrow R$ such that $f^-1(x)+f(x)=x \forall x\in R$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_13916 : ∃ f : ℝ → ℝ, Function.Injective f ∧ ∀ x, f x + f⁻¹ x = x   :=  by sorry

Represent a functional inverse by a second function g with g∘f=id and f∘g=id, and require f(x)+g(x)=x; do not use the pointwise multiplicative inverse notation.

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

Proposed corrected statement

Represent a functional inverse by a second function g with g∘f=id and f∘g=id, and require f(x)+g(x)=x; do not use the pointwise multiplicative inverse notation.

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.