Definitions hol bool Sections HOLlib Doc
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Some definitions of interest.
bexistsDef x:TP(x) == (x:TP(x))
Thm* T:Type, P:(T). (x:TP(x))  
stypeDef S == {T:Type| x:T. True }
Thm* S  Type{2}

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boolsetfunctionuniversemembertrueallexists!abstraction
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Definitions hol bool Sections HOLlib Doc