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@ctchou ctchou commented Jan 15, 2026

This PR lays some groundwork for proving the closure of omega-regular languages under complementation. The main result is IsRegular.fin_cover_saturates_compl in OmegaRegularLanguage.lean, which depends on the definition and theorems in Saturation.lean.

In future work we will construct a right congruence of finite index on finite words so that the index type I in IsRegular.fin_cover_saturates_compl consists of pairs of equivalence classes of this congruence.

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My comments have been addressed.

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