
theorem
  for I be non empty set, M be non-empty ManySortedSet of I holds
  M = EmptyMS I +* (M|support M)
proof
  let I be non empty set, M be non-empty ManySortedSet of I;
  set MM = M|support M;
A1: I c= support M
  proof
    let v be object;
    assume
A2: v in I;
    then M.v <> {};
    hence thesis by A2;
  end;
  dom M = I by PARTFUN1:def 2;
  then MM = M by A1,RELAT_1:68;
  hence thesis by Th1;
end;
