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;

theorem
  Y is empty-yielding & X c= Y implies X is empty-yielding
proof
  assume
A1: Y is empty-yielding & X c= Y;
  let i be object;
  assume i in I;
  then X.i c= Y.i & Y.i is empty by A1;
  hence thesis;
end;
