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;
