set s = { (Sub . A) where A is Element of LTLB_WFF : A in X } ;
{ (Sub . A) where A is Element of LTLB_WFF : A in X } c= bool LTLB_WFF

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { (Sub . A) where A is Element of LTLB_WFF : A in X } or x in bool LTLB_WFF )
assume x in { (Sub . A) where A is Element of LTLB_WFF : A in X } ; :: thesis: x in bool LTLB_WFF
then ex A being Element of LTLB_WFF st
( x = Sub . A & A in X ) ;
hence x in bool LTLB_WFF ; :: thesis: verum

end;

hence { (Sub . A) where A is Element of LTLB_WFF : A in X } is Subset of (bool LTLB_WFF) ; :: thesis: verum