reserve a, I for set,
  S for non empty non void ManySortedSign;

theorem Th9:
  for A being non-empty ManySortedSet of I, B being ManySortedSet
  of I for F being ManySortedFunction of A, {B} holds F is "onto"
proof
  let A be non-empty ManySortedSet of I, B be ManySortedSet of I, F be
  ManySortedFunction of A, {B};
  let i be set;
  assume
A1: i in I;
  then {B}.i = {B.i} & F.i is Function of A.i, {B}.i by PBOOLE:def 15
,PZFMISC1:def 1;
  hence thesis by A1,Th2;
end;
