Equidecomposable_Nested_Sets

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Let A, B, C be sets such that A and C are equidecomposable and A subset B subset C. Then B and C are equidecomposable.

Why this node was retired

The posted statement is

theorem Equidecomposable_Nested_Sets {α : Type _} (A B C : Set α) (hAC : ∃ f : A ≃ C, True) (hAB : A ⊆ B) (hBC : B ⊆ C) : ∃ g : B ≃ C, True := by sorry

Geometric equidecomposability has been replaced by existence of an arbitrary bijection; the proof applies set-theoretic Schröder–Bernstein.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

For a specified group of isometries acting on the ambient space, define equidecomposability by finite partitions and piecewise actions. If A⊆B⊆C and A,C are equidecomposable in that sense, state the corresponding equidecomposability conclusion for B,C, with the geometric convention fixed.

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.