reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem Th7:
  for I being set, M being ManySortedSet of I for i being set st i
  in I holds i.--> (M.i) = M|{i}
proof
  let I be set, M be ManySortedSet of I, i be set;
  assume i in I;
  then i in dom M by PARTFUN1:def 2;
  hence thesis by Th6;
end;
