assume A1: X <> {} ; :: thesis: { x where x is Element of X : n <= #occurrences (x,A) } is List of X
{ x where x is Element of X : n <= #occurrences (x,A) } c= X
proof
let z be object ; :: according to TARSKI:def 3 :: thesis: ( not z in { x where x is Element of X : n <= #occurrences (x,A) } or z in X )
assume z in { x where x is Element of X : n <= #occurrences (x,A) } ; :: thesis: z in X
then ex x being Element of X st
( z = x & n <= #occurrences (x,A) ) ;
hence z in X by A1; :: thesis: verum
end;
hence { x where x is Element of X : n <= #occurrences (x,A) } is List of X ; :: thesis: verum