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
  X is non-empty & X [= Y implies Y is non-empty
proof
  assume
A1: X is non-empty;
  assume X [= Y;
  then X c= Y by A1,Th132;
  hence thesis by A1,Th131;
end;
