assume A2:
X <> {}
; :: thesis: { x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } is List of X

{ x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } c= X

{ x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } c= X

proof

hence
{ x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } 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 : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } or z in X )

assume z in { x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } ; :: thesis: z in X

then ex x being Element of X st

( z = x & n <= #occurrences (x,A) & #occurrences (x,A) <= m ) ;

hence z in X by A2; :: thesis: verum

end;assume z in { x where x is Element of X : ( n <= #occurrences (x,A) & #occurrences (x,A) <= m ) } ; :: thesis: z in X

then ex x being Element of X st

( z = x & n <= #occurrences (x,A) & #occurrences (x,A) <= m ) ;

hence z in X by A2; :: thesis: verum