assume A2: the carrier of X <> {} ; :: thesis: { x where x is Element of X : ( card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) } is List of X
{ x where x is Element of X : ( card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) } c= the carrier of X

proof

let z be object ; :: according to TARSKI:def 3 :: thesis: ( not z in { x where x is Element of X : ( card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) } or z in the carrier of X )
assume z in { x where x is Element of X : ( card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) } ; :: thesis: z in the carrier of X
then ex x being Element of X st
( z = x & card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) ;
hence z in the carrier of X by A2; :: thesis: verum

end;

hence { x where x is Element of X : ( card ((x ref) \ (rng A)) <= n & card ((rng A) \ (x ref)) <= m ) } is List of X ; :: thesis: verum