reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th3:
  (for i being object st i in I holds X.i = Y.i) implies X = Y
proof
  dom X = I & dom Y = I by PARTFUN1:def 2;
  hence thesis;
end;
