chore: add the consequences of an empty alphabet type on Language and OmegaLanguage - #722
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… OmegaLanguage (#722) This PR proves some consequences of an empty alphabet type (denoted by `Symbol`) on Language and OmegaLanguage: (1) The only possible languages over an empty alphabet are {} and {[]}. (2) The only possible omega-language over an empty alphabet is {}. Furthermore, (1) enables the assumption `[Inhabited Symbol]` to be removed from the regular language closure properties `IsRegular.mul` and `IsRegular.kstar`. Now no closure property for regular languages has that assumption.
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This PR proves some consequences of an empty alphabet type (denoted by
Symbol) on Language and OmegaLanguage:(1) The only possible languages over an empty alphabet are {} and {[]}.
(2) The only possible omega-language over an empty alphabet is {}.
Furthermore, (1) enables the assumption
[Inhabited Symbol]to be removed from the regular language closure propertiesIsRegular.mulandIsRegular.kstar. Now no closure property for regular languages has that assumption.