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

theorem
  for A, B being ManySortedSet of I for F, G being ManySortedFunction of
  A, {B} holds F = G
proof
  let A, B be ManySortedSet of I, F, G be ManySortedFunction of A, {B};
  now
    let i be object;
    assume
A1: i in I;
    then
A2: {B}.i = {B.i} by PZFMISC1:def 1;
    F.i is Function of A.i, {B}.i & G.i is Function of A.i, {B}. i by A1,
PBOOLE:def 15;
    hence F.i = G.i by A2,FUNCT_2:51;
  end;
  hence thesis;
end;
