Relation_Isomorphism_is_Equivalence_Relation

⚠️ 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.

Relation isomorphism is an equivalence relation.

Why this node was retired

The posted statement is

theorem Relation_Isomorphism_is_Equivalence_Relation {α : Type _} (R : α → α → Prop) : Equivalence (fun a b => R a b ↔ R b a) := by sorry

The relation R(a,b)↔R(b,a) on one set is not isomorphism of relational structures.

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

Proposed corrected statement

Define A∼B for relational structures A,B iff there exists a bijection preserving and reflecting their relations, and prove this relation is reflexive, symmetric and transitive. The target predicate must be replaced, not supplemented with arbitrary assumptions on R.

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.