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,Y being non empty set, M be Y-valued ManySortedSet of I,
     x be Element of I
  holds M.x = M/.x
proof
  let I,Y be non empty set, M be Y-valued ManySortedSet of I,
     x be Element of I;
  dom M = I by PARTFUN1:def 2;
  hence M.x = M/.x by PARTFUN1:def 6;
end;
