set US = { F where F is Filter of L : F is prime } ;
{ F where F is Filter of L : F is prime } c= bool the carrier of L

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { F where F is Filter of L : F is prime } or x in bool the carrier of L )
assume x in { F where F is Filter of L : F is prime } ; :: thesis: x in bool the carrier of L
then ex UF being Filter of L st
( UF = x & UF is prime ) ;
hence x in bool the carrier of L ; :: thesis: verum

end;

hence { F where F is Filter of L : F is prime } is Subset-Family of L ; :: thesis: verum