set A = { F where F is Filter of L : a in F } ;
{ F where F is Filter of L : a in F } 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 : a in F } or x in bool the carrier of L )
assume x in { F where F is Filter of L : a in F } ; :: thesis: x in bool the carrier of L
then ex F being Filter of L st
( x = F & a in F ) ;
hence x in bool the carrier of L ; :: thesis: verum

end;

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