feat: prove that the Buchi congruence has the saturation property#325
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ctchou wants to merge 50 commits intoleanprover:mainfrom
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feat: prove that the Buchi congruence has the saturation property#325ctchou wants to merge 50 commits intoleanprover:mainfrom
ctchou wants to merge 50 commits intoleanprover:mainfrom
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…n of omega-languages of a special form
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…d fix merge conflicts
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Feb 18, 2026
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As I mention I've not fully reviewed buchiFamily_saturation, but here is an initial review.
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This PR proves that the Buchi congruence introduced in #278 has the saturation property defined in
Cslib.Foundations.Data.Set.Saturation. More precisely, the family of omega-languages of the formU * V^ω, whereUandVare equivalence classes of the Buchi congruence, saturates the omega-language accepted by the underlying Buchi automaton. This proof is the hardest step in proving the closure of ω-regular languages under complementation and explains why the Buchi congruence is defined the way it is. Some miscellaneous results about LTS and infinite sequences that are needed by the proof are also added.