{ x where x is Element of X : ( card (x . O) = n & x in L ) } c= X

proof

hence
{ x where x is Element of X : ( card (x . O) = n & x in L ) } is List of X
; :: thesis: verum
let z be object ; :: according to TARSKI:def 3 :: thesis: ( not z in { x where x is Element of X : ( card (x . O) = n & x in L ) } or z in X )

assume z in { x where x is Element of X : ( card (x . O) = n & x in L ) } ; :: thesis: z in X

then ex x being Element of X st

( z = x & card (x . O) = n & x in L ) ;

hence z in X ; :: thesis: verum

end;assume z in { x where x is Element of X : ( card (x . O) = n & x in L ) } ; :: thesis: z in X

then ex x being Element of X st

( z = x & card (x . O) = n & x in L ) ;

hence z in X ; :: thesis: verum