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Let $\Delta = \lambda x.(x)x$ and consider $\Omega = (\Delta)\Delta$. Then $\Omega$ is exactly the only $\lambda$-term of the form $(\lambda x.t)v$ such that $(\lambda x.t)v=t\{v\ /\ x\}$.

Does someone have references about this statement ? I could not find something enough relevant in my ressources or in my lectures material.

Thanks in advance !

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  • $\begingroup$ Cross-posted at cstheory.SE which seems the better place than here $\endgroup$ Dec 14, 2021 at 18:01

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