reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;
reserve I for non empty set,
  x,X,Y for ManySortedSet of I;
reserve I for set,
  x,X,Y,Z for ManySortedSet of I;
reserve X for non-empty ManySortedSet of I;
reserve D for non empty set,
  n for Nat;
reserve X,Y for ManySortedSet of I;

theorem
  for I,A be set
  for s,ss being ManySortedSet of I
  holds (ss +* s | A) | A = s | A
proof
  let I,A be set;
  let s,ss be ManySortedSet of I;
  dom s = I by PARTFUN1:def 2
    .= dom ss by PARTFUN1:def 2;
  then A /\ dom ss c= A /\ dom s;
  hence thesis by FUNCT_4:88;
end;
