Mostowski collapse lemma

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The Mostowski collapse lemma in mathematical logic states that for any structure S with a well-founded relation R, such that

{y : y R x}

is a set, and such that R satisfies extensionality, there exists a transitive class C (possibly proper) whose structure under the membership relation is isomorphic to S. The isomorphism maps each element x of S to the set of images of elements y of S such that

y R x.

It is named for Andrzej Mostowski.