let BL be non trivial B_Lattice; :: thesis: for a being Element of BL holds { F where F is Filter of BL : ( F is being_ultrafilter & a in F ) } c= ultraset BL
let a be Element of BL; :: thesis: { F where F is Filter of BL : ( F is being_ultrafilter & a in F ) } c= ultraset BL
let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in { F where F is Filter of BL : ( F is being_ultrafilter & a in F ) } or x in ultraset BL )
assume x in { F where F is Filter of BL : ( F is being_ultrafilter & a in F ) } ; :: thesis: x in ultraset BL
then consider UF being Filter of BL such that
A1: ( UF = x & UF is being_ultrafilter & a in UF ) ;
thus x in ultraset BL by A1; :: thesis: verum